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Viscoelastic Pipe Flow is Linearly Unstable @article{GarChaKhaShaSubPRL2018, author = {Garg, Piyush and Chaudhary, Indresh and Khalid, Mohammad and Shankar, V. and Subramanian, Ganesh}, title = {Viscoelastic Pipe Flow is Linearly Unstable}, journal = {Phys. Rev. Lett.}, publisher = {American Physical Society}, year = {2018}, volume = {121}, pages = {024502}, doi = {https://doi.org/10.1103/PhysRevLett.121.024502} }
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Streak evolution in viscoelastic Couette flow @article{pagzakJFM2014, author = {Page, Jacob and Zaki, Tamer A.}, title = {Streak evolution in viscoelastic Couette flow}, journal = {J. Fluid Mech.}, publisher = {Cambridge University Press}, year = {2014}, volume = {742}, pages = {520-551}, doi = {https://doi.org/10.1017/jfm.2013.686} }
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An introduction to partial differential equations @book{pinchover2005introduction, author = {Pinchover, Yehuda and Rubinstein, Jacob}, title = {An introduction to partial differential equations}, publisher = {Cambridge University Press}, year = {2005} }
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Turbulent channel flow near maximum drag reduction: Simulations, experiments and mechanisms @article{huntJFM2003, author = {Ptasinski, P. K. and Boersma, B. J. and Nieuwstadt, F. T. M. and Hulsen, M. A. and Van Den Brule, B. H. A. A. and Hunt, J. C. R.}, title = {Turbulent channel flow near maximum drag reduction: Simulations, experiments and mechanisms}, journal = {J. Fluid Mech.}, publisher = {Cambridge University Press}, year = {2003}, volume = {490}, pages = {251-291}, doi = {https://doi.org/10.1017/S0022112003005305} }
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Flow Resistance and Structures in Viscoelastic Channel Flows at Low Re @article{qin2019elastic, author = {Qin, Boyang and Salipante, Paul F. and Hudson, Steven D. and Arratia, Paulo E.}, title = {Flow Resistance and Structures in Viscoelastic Channel Flows at Low Re}, journal = {Phys. Rev. Lett.}, publisher = {American Physical Society}, year = {2019}, volume = {123}, pages = {194501}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.194501}, doi = {https://doi.org/10.1103/PhysRevLett.123.194501} }
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VORTICES, STABILITY, AND TURBULENCE @article{SaffmanVortices, author = {P. G. Saffman}, title = {VORTICES, STABILITY, AND TURBULENCE}, journal = {Ann. N. Y. Acad. Sci.}, publisher = {Wiley Online Library}, year = {1983}, volume = {404}, pages = {12-24}, doi = {https://doi.org/10.1111/j.1749-6632.1983.tb19411.x} }
Nonmodal Stability Theory @article{SchmidARFM2007, author = {Schmid, Peter J.}, title = {Nonmodal Stability Theory}, journal = {Annu. Rev. Fluid Mech.}, year = {2007}, pages = {129-162}, doi = {https://doi.org/10.1146/annurev.fluid.38.050304.092139} }
Stability and transition in shear flows @book{schmid2012stability, author = {Schmid, Peter J and Henningson, Dan S}, title = {Stability and transition in shear flows}, publisher = {Springer Science and Business Media}, year = {2012} }
Optimal energy density growth in HagenāPoiseuille flow @article{schmid_henningson_1994, author = {Schmid, Peter J. and Henningson, Dan S.}, title = {Optimal energy density growth in HagenāPoiseuille flow}, journal = {J. Fluid Mech.}, publisher = {Cambridge University Press}, year = {1994}, volume = {277}, pages = {197-225}, doi = {https://doi.org/10.1017/S0022112094002739} }
Critical-Layer Structures and Mechanisms in Elastoinertial Turbulence @article{shekar2019, author = {Shekar, Ashwin and McMullen, Ryan M. and Wang, Sung-Ning and McKeon, Beverley J. and Graham, Michael D.}, title = {Critical-Layer Structures and Mechanisms in Elastoinertial Turbulence}, journal = {Phys. Rev. Lett.}, publisher = {American Physical Society}, year = {2019}, volume = {122}, pages = {124503}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.124503}, doi = {https://doi.org/10.1103/PhysRevLett.122.124503} }
Spectral methods: Algorithms, analysis and applications @book{shen2011spectral, author = {Shen, Jie and Tang, Tao and Wang, Li-Lian}, title = {Spectral methods: Algorithms, analysis and applications}, publisher = {Springer Science and Business Media}, year = {2011} }
Multivariable feedback control: Analysis and design @book{skogestad2007multivariable, author = {Skogestad, Sigurd and Postlethwaite, Ian}, title = {Multivariable feedback control: Analysis and design}, publisher = {Wiley}, year = {2007} }
A Jacobi–Davidson iteration method for linear eigenvalue problems @article{sleijpen2000jacobi, author = {Sleijpen, Gerard L G and Van der Vorst, Henk A}, title = {A Jacobi--Davidson iteration method for linear eigenvalue problems}, journal = {SIAM Rev.}, publisher = {SIAM}, year = {2000}, volume = {42}, pages = {267-293} }
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Sparsity-promoting dynamic mode decomposition for systems with inputs @inproceedings{annseijovCDC16, author = {J. Annoni and P. Seiler and M. R. Jovanović}, title = {Sparsity-promoting dynamic mode decomposition for systems with inputs}, booktitle = {Proceedings of the 55th IEEE Conference on Decision and Control}, year = {2016}, pages = {6506-6511}, note = {(Invited paper)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/annseijovCDC16.pdf} }
Coherence in large-scale networks: dimension dependent limitations of local feedback @article{bamjovmitpat12, author = {B. Bamieh and M. R. Jovanović and P. Mitra and S. Patterson}, title = {Coherence in large-scale networks: dimension dependent limitations of local feedback}, journal = {IEEE Trans. Automat. Control}, year = {2012}, volume = {57}, number = {9}, pages = {2235-2249}, note = {(2013 George S.\ Axelby Outstanding Paper Award)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/bamjovmitpatTAC12.pdf} }
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PWM control of hydraulic cylinder and axial piston hydraulic motor @inproceedings{cebjov97, author = {N. A. Cebasek and M. R. Jovanović}, title = {PWM control of hydraulic cylinder and axial piston hydraulic motor}, booktitle = {Proceedings of the 5th Triennial International Symposium on Fluid Control, Measurement and Visualization}, year = {1997}, volume = {1}, pages = {361-366} }
State covariances and the matrix completion problem @inproceedings{chejovgeoCDC13, author = {Y. Chen and M. R. Jovanović and T. T. Georgiou}, title = {State covariances and the matrix completion problem}, booktitle = {Proceedings of the 52nd IEEE Conference on Decision and Control}, year = {2013}, pages = {1702-1707} }
Guest Editorial Special Issue on Analysis, Control, and Optimization of Energy Networks @article{guestTCNS19, author = {M. Chertkov and M. R. Jovanović and B. Lesieutre and S. Low and P. van Hentenryck and L. Wehenkel}, title = {Guest Editorial Special Issue on Analysis, Control, and Optimization of Energy Networks}, journal = {IEEE Trans. Control Netw. Syst.}, year = {2019}, volume = {6}, number = {3}, pages = {922-924}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/guestTCNS19.pdf} }
Convex reformulation of a robust optimal control problem for a class of positive systems @inproceedings{coldhijovsmiCDC16, author = {M. Colombino and N.K. Dhingra and M. R. Jovanović and R. S. Smith}, title = {Convex reformulation of a robust optimal control problem for a class of positive systems}, booktitle = {Proceedings of the 55th IEEE Conference on Decision and Control}, year = {2016}, pages = {5263-5268}, note = {(Invited paper)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/coldhijovsmiCDC16.pdf} }
On the optimal control problem for a class of monotone bilinear systems @inproceedings{coldhijovransmiMTNS16, author = {M. Colombino and N. K. Dhingra and M. R. Jovanović and A. Rantzer and R. S. Smith}, title = {On the optimal control problem for a class of monotone bilinear systems}, booktitle = {Proceedings of the 22nd International Symposium on Mathematical Theory of Network and Systems}, year = {2016}, pages = {411-413}, note = {(Invited paper)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/coldhijovransmiMTNS16.pdf} }
The inaugural CDC soccer cup @article{coregejovCSM19, author = {J. Cortes and M. Egerstedt and M. R. Jovanović}, title = {The inaugural CDC soccer cup}, journal = {IEEE Control Syst. Mag.}, year = {2019}, volume = {39}, number = {3}, pages = {17-39}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/coregejovCSM19.pdf} }
Non-Lyapunov stability consideration of linear descriptor systems operating under perturbing forces @article{debjov97, author = {D. Debeljković and M. R. Jovanović}, title = {Non-Lyapunov stability consideration of linear descriptor systems operating under perturbing forces}, journal = {Advances in Modeling and Analysis}, year = {1997}, volume = {49}, number = {1-2}, pages = {1-8} }
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State and noise covariance estimation in power grids using limited nodal PMUs @inproceedings{dekzarlokjovcheGSIP17, author = {D. Deka and A. Zare and A. Lokhov and M. R. Jovanović and M. Chertkov}, title = {State and noise covariance estimation in power grids using limited nodal PMUs}, booktitle = {Proceedings of the 5th IEEE Global Conference on Signal and Information Processing}, year = {2017}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dekzarlokjovcheGSIP17.pdf} }
Optimization and control of large-scale networked systems @phdthesis{neil-phd17, author = {N. K. Dhingra}, title = {Optimization and control of large-scale networked systems}, institution = {University of Minnesota}, school = {University of Minnesota}, year = {2017}, pdf = {/viterbi-web.usc.edu/~mihailo/theses/NeilDhingra-PhD.pdf} }
Structured decentralized control of positive systems with applications to combination drug therapy and leader selection in directed networks @article{dhicoljovTCNS19, author = {N. K. Dhingra and M. Colombino and M. R. Jovanović}, title = {Structured decentralized control of positive systems with applications to combination drug therapy and leader selection in directed networks}, journal = {IEEE Trans. Control Netw. Syst.}, year = {2019}, volume = {6}, number = {1}, pages = {352-362}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dhicoljovTCNS19.pdf} }
Leader selection in directed networks @inproceedings{dhicoljovCDC16, author = {N. K. Dhingra and M. Colombino and M. R. Jovanović}, title = {Leader selection in directed networks}, booktitle = {Proceedings of the 55th IEEE Conference on Decision and Control}, year = {2016}, pages = {2715-2720}, note = {(Invited paper)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dhicoljovCDC16.pdf} }
On the convexity of a class of structured optimal control problems for positive systems @inproceedings{dhicoljovECC16, author = {N. K. Dhingra and M. Colombino and M. R. Jovanović}, title = {On the convexity of a class of structured optimal control problems for positive systems}, booktitle = {Proceedings of the 2016 European Control Conference}, year = {2016}, pages = {825-830}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dhicoljovECC16.pdf} }
On the optimal control problem for a class of monotone bilinear systems @article{dhicoljovransmiSCL16, author = {N. K. Dhingra and M. Colombino and M. R. Jovanović and A. Rantzer and R. S. Smith}, title = {On the optimal control problem for a class of monotone bilinear systems}, journal = {Syst. Control Lett.}, year = {2016}, note = {submitted; also arXiv:1611.09984}, pdf = {/arxiv.org/abs/1611.09984} }
A method of multipliers algorithm for sparsity-promoting optimal control @inproceedings{dhijovACC16, author = {N. K. Dhingra and M. R. Jovanović}, title = {A method of multipliers algorithm for sparsity-promoting optimal control}, booktitle = {Proceedings of the 2016 American Control Conference}, year = {2016}, pages = {1942-1947}, note = {(Invited paper)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dhijovACC16.pdf} }
Convex synthesis of symmetric modifications to linear systems @inproceedings{dhijovACC15, author = {N. K. Dhingra and M. R. Jovanović}, title = {Convex synthesis of symmetric modifications to linear systems}, booktitle = {Proceedings of the 2015 American Control Conference}, year = {2015}, pages = {3583-3588}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dhijovACC15.pdf} }
Optimal sensor and actuator selection for large-scale dynamical systems @inproceedings{dhijovluoASI15, author = {N. K. Dhingra and M. R. Jovanović and Z. Q. Luo}, title = {Optimal sensor and actuator selection for large-scale dynamical systems}, booktitle = {Proceedings of the 2015 Asilomar Conference on Signals, Systems, and Computers}, year = {2015}, note = {to appear} }
An ADMM algorithm for optimal sensor and actuator selection @inproceedings{dhijovluoCDC14, author = {N. K. Dhingra and M. R. Jovanović and Z. Q. Luo}, title = {An ADMM algorithm for optimal sensor and actuator selection}, booktitle = {Proceedings of the 53rd IEEE Conference on Decision and Control}, year = {2014}, pages = {4039-4044}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dhijovluoCDC14.pdf} }
The proximal augmented Lagrangian method for nonsmooth composite optimization @article{dhikhojovTAC19, author = {N. K. Dhingra and S. Z. Khong and M. R. Jovanović}, title = {The proximal augmented Lagrangian method for nonsmooth composite optimization}, journal = {IEEE Trans. Automat. Control}, year = {2019}, volume = {64}, number = {7}, pages = {2861-2868}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dhikhojovTAC19.pdf} }
A second order primal-dual algorithm for non-smooth convex composite optimization @inproceedings{dhikhojovCDC17, author = {N. K. Dhingra and S. Z. Khong and M. R. Jovanović}, title = {A second order primal-dual algorithm for non-smooth convex composite optimization}, booktitle = {Proceedings of the 56th IEEE Conference on Decision and Control}, year = {2017}, pages = {2868-2873}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dhikhojovCDC17.pdf} }
A second order primal-dual method for nonsmooth convex composite optimization @article{dhikhojovTAC17, author = {N. K. Dhingra and S. Z. Khong and M. R. Jovanović}, title = {A second order primal-dual method for nonsmooth convex composite optimization}, journal = {IEEE Trans. Automat. Control}, year = {2017}, note = {conditionally accepted; also arXiv:1709.01610}, pdf = {/arxiv.org/abs/1709.01610} }
On identifying sparse representations of consensus networks @inproceedings{dhilinfarjovIFAC12, author = {N. K. Dhingra and F. Lin and M. Fardad and M. R. Jovanović}, title = {On identifying sparse representations of consensus networks}, booktitle = {Preprints of the 3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems}, year = {2012}, pages = {305-310}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/conference/2012/DhingraLinFardadJovanovicIFAC2012.pdf} }
Sparsity-promoting optimal control of systems with invariances and symmetries @inproceedings{dhiwujovNOL16, author = {N. K. Dhingra and X. Wu and M. R. Jovanović}, title = {Sparsity-promoting optimal control of systems with invariances and symmetries}, booktitle = {Proceedings of the 10th IFAC Symposium on Nonlinear Control Systems}, year = {2016}, pages = {648-653} }
An exponentially convergent primal-dual algorithm for nonsmooth composite minimization @inproceedings{dinhudhijovCDC18, author = {D. Ding and B. Hu and N. K. Dhingra and M. R. Jovanović}, title = {An exponentially convergent primal-dual algorithm for nonsmooth composite minimization}, booktitle = {Proceedings of the 57th IEEE Conference on Decision and Control}, year = {2018}, pages = {4927-4932}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dinhudhijovCDC18.pdf} }
Global exponential stability of primal-dual gradient flow dynamics based on the proximal augmented Lagrangian @inproceedings{dinjovACC19, author = {D. Ding and M. R. Jovanović}, title = {Global exponential stability of primal-dual gradient flow dynamics based on the proximal augmented Lagrangian}, booktitle = {Proceedings of the 2019 American Control Conference}, year = {2019}, pages = {3414-3419}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dinjovACC19.pdf} }
Global exponential stability of primal-dual gradient flow dynamics based on the proximal augmented Lagrangian: A Lyapunov-based approach @article{dinjovLCSS19, author = {D. Ding and M. R. Jovanović}, title = {Global exponential stability of primal-dual gradient flow dynamics based on the proximal augmented Lagrangian: A Lyapunov-based approach}, journal = {IEEE Control Syst. Lett.}, year = {2019}, note = {submitted; also arXiv:1910.00783}, pdf = {/arxiv.org/abs/1910.00783} }
A primal-dual Laplacian gradient flow dynamics for distributed resource allocation problems @inproceedings{dinjovACC18, author = {D. Ding and M. R. Jovanović}, title = {A primal-dual Laplacian gradient flow dynamics for distributed resource allocation problems}, booktitle = {Proceedings of the 2018 American Control Conference}, year = {2018}, pages = {5316-5320}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dinjovACC18.pdf} }
Distributed robust statistical learning: Byzantine mirror descent @inproceedings{dinweijovCDC19, author = {D. Ding and X. Wei and M. R. Jovanović}, title = {Distributed robust statistical learning: Byzantine mirror descent}, booktitle = {Proceedings of the 58th IEEE Conference on Decision and Control}, year = {2019}, pages = {1822-1827}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dinweijovCDC19.pdf} }
Provably efficient safe exploration via primal-dual policy optimization @inproceedings{dinweiyanwanjovICML20, author = {D. Ding and X. Wei and Z. Yang and Z. Wang and M. R. Jovanović}, title = {Provably efficient safe exploration via primal-dual policy optimization}, booktitle = {37th International Conference on Machine Learning}, year = {2020} }
Fast multi-agent temporal-difference learning via homotopy stochastic primal-dual method @inproceedings{dinweiyanwanjovNIPS19, author = {D. Ding and X. Wei and Z. Yang and Z. Wang and M. R. Jovanović}, title = {Fast multi-agent temporal-difference learning via homotopy stochastic primal-dual method}, booktitle = {Optimization Foundations for Reinforcement Learning Workshop, 33rd Conference on Neural Information Processing Systems}, year = {2019}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dinweiyanwanjovNIPS19.pdf} }
Sparsity-promoting optimal wide-area control of power networks @article{dorjovchebulTPS14, author = {F. Dörfler and M. R. Jovanović and M. Chertkov and F. Bullo}, title = {Sparsity-promoting optimal wide-area control of power networks}, journal = {IEEE Trans. Power Syst.}, year = {2014}, volume = {29}, number = {5}, pages = {2281-2291}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dorjovchebulTPS14.pdf} }
Sparse and optimal wide-area damping control in power networks @inproceedings{dorjovchebulACC13, author = {F. Dörfler and M. R. Jovanović and M. Chertkov and F. Bullo}, title = {Sparse and optimal wide-area damping control in power networks}, booktitle = {Proceedings of the 2013 American Control Conference}, year = {2013}, pages = {4295-4300}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dorjovchebulACC13.pdf} }
A frequency domain analysis of compressible linearized Navier-Stokes equations in a hypersonic compression ramp flow @inproceedings{dwicanjovACC20, author = {A. Dwivedi and G. V. Candler and M. R. Jovanović}, title = {A frequency domain analysis of compressible linearized Navier-Stokes equations in a hypersonic compression ramp flow}, booktitle = {Proceedings of the 2020 American Control Conference}, year = {2020}, note = {to appear} }
Optimal spatial growth of streaks in oblique shockboundary layer interaction/ @inproceedings{dwinicjovcanAIAA17, author = {A. Dwivedi and J. W. Nichols and M. R. Jovanović and G. V. Candler}, title = {Optimal spatial growth of streaks in oblique shock/boundary layer interaction}, booktitle = {Proceedings of the 47th AIAA Fluid Dynamics Conference}, year = {2017}, pages = {4163 (17 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dwinicjovcanAIAA17.pdf} }
Input-output analysis of shock boundary layer interaction @inproceedings{dwisidcannicjovAIAA18, author = {A. Dwivedi and G. S. Sidharth and G. V. Candler and J. W. Nichols and M. R. Jovanović}, title = {Input-output analysis of shock boundary layer interaction}, booktitle = {Proceedings of the 48th AIAA Fluid Dynamics Conference}, year = {2018}, pages = {3220 (17 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dwisidcannicjovAIAA18.pdf} }
Reattachment vortices in hypersonic compression ramp flow: an input-output analysis @article{dwisidniccanjovJFM19, author = {A. Dwivedi and G. S. Sidharth and J. W. Nichols and G. V. Candler and M. R. Jovanović}, title = {Reattachment vortices in hypersonic compression ramp flow: an input-output analysis}, journal = {J. Fluid Mech.}, year = {2019}, volume = {880}, pages = {113-135}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/dwisidniccanjovJFM19.pdf} }
On the design of optimal structured and sparse feedback gains using semidefinite programming @inproceedings{farjovACC14, author = {M. Fardad and M. R. Jovanović}, title = {On the design of optimal structured and sparse feedback gains using semidefinite programming}, booktitle = {Proceedings of the 2014 American Control Conference}, year = {2014}, pages = {2438-2443} }
Design of optimal controllers for spatially invariant systems with finite communication speed @article{farjovAUT11, author = {M. Fardad and M. R. Jovanović}, title = {Design of optimal controllers for spatially invariant systems with finite communication speed}, journal = {Automatica}, year = {2011}, volume = {47}, number = {5}, pages = {880-889}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/farjovAUT11.pdf} }
On the state-space design of optimal controllers for distributed systems with finite communication speed @inproceedings{farjovCDC08, author = {M. Fardad and M. R. Jovanović}, title = {On the state-space design of optimal controllers for distributed systems with finite communication speed}, booktitle = {Proceedings of the 47th IEEE Conference on Decision and Control}, year = {2008}, pages = {5488-5493}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/farjovCDC08.pdf} }
Frequency analysis and norms of distributed spatially periodic systems @article{farjovbam08, author = {M. Fardad and M. R. Jovanović and B. Bamieh}, title = {Frequency analysis and norms of distributed spatially periodic systems}, journal = {IEEE Trans. Automat. Control}, year = {2008}, volume = {53}, number = {10}, pages = {2266-2279}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/tac08periodic.pdf} }
Damping mechanisms in dynamic mode atomic force microscopy applications @inproceedings{farjovsalACC09, author = {M. Fardad and M. R. Jovanović and M. V. Salapaka}, title = {Damping mechanisms in dynamic mode atomic force microscopy applications}, booktitle = {Proceedings of the 2009 American Control Conference}, year = {2009}, pages = {2272-2277} }
Design of optimal sparse interconnection graphs for synchronization of oscillator networks @article{farlinjovTAC14sync, author = {M. Fardad and F. Lin and M. R. Jovanović}, title = {Design of optimal sparse interconnection graphs for synchronization of oscillator networks}, journal = {IEEE Trans. Automat. Control}, year = {2014}, volume = {59}, number = {9}, pages = {2457-2462}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/farlinjovTAC14sync.pdf} }
On optimal link creation for facilitation of consensus in social networks @inproceedings{farlinjovACC14, author = {M. Fardad and F. Lin and M. R. Jovanović}, title = {On optimal link creation for facilitation of consensus in social networks}, booktitle = {Proceedings of the 2014 American Control Conference}, year = {2014}, pages = {3802-3807} }
On the optimal synchronization of oscillator networks via sparse interconnection graphs @inproceedings{farlinjovACC12, author = {M. Fardad and F. Lin and M. R. Jovanović}, title = {On the optimal synchronization of oscillator networks via sparse interconnection graphs}, booktitle = {Proceedings of the 2012 American Control Conference}, year = {2012}, pages = {4777-4782} }
Algorithms for leader selection in large dynamical networks: noise-free leaders @inproceedings{farlinjovCDC11, author = {M. Fardad and F. Lin and M. R. Jovanović}, title = {Algorithms for leader selection in large dynamical networks: noise-free leaders}, booktitle = {Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference}, year = {2011}, pages = {7188-7193}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/farlinjovCDC11.pdf} }
Sparsity-promoting optimal control for a class of distributed systems @inproceedings{farlinjovACC11, author = {M. Fardad and F. Lin and M. R. Jovanović}, title = {Sparsity-promoting optimal control for a class of distributed systems}, booktitle = {Proceedings of the 2011 American Control Conference}, year = {2011}, pages = {2050-2055}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/farlinjovACC11.pdf} }
On the dual decomposition of linear quadratic optimal control problems for vehicular formations @inproceedings{farlinjovCDC10, author = {M. Fardad and F. Lin and M. R. Jovanović}, title = {On the dual decomposition of linear quadratic optimal control problems for vehicular formations}, booktitle = {Proceedings of the 49th IEEE Conference on Decision and Control}, year = {2010}, pages = {6287-6292} }
On the optimal design of structured feedback gains for interconnected systems @inproceedings{farlinjovCDC09, author = {M. Fardad and F. Lin and M. R. Jovanović}, title = {On the optimal design of structured feedback gains for interconnected systems}, booktitle = {Proceedings of the 48th IEEE Conference on Decision and Control}, year = {2009}, pages = {978-983} }
On new characterizations of social influence in social networks @inproceedings{farlinzhajovACC13, author = {M. Fardad and F. Lin and X. Zhang and M. R. Jovanović}, title = {On new characterizations of social influence in social networks}, booktitle = {Proceedings of the 2013 American Control Conference}, year = {2013}, pages = {4784-4789} }
On the properties of optimal weak links in consensus networks @inproceedings{farzhalinjovCDC14, author = {M. Fardad and X. Zhang and F. Lin and M. R. Jovanović}, title = {On the properties of optimal weak links in consensus networks}, booktitle = {Proceedings of the 53rd IEEE Conference on Decision and Control}, year = {2014}, pages = {2124-2129}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/farzhalinjovCDC14.pdf} }
On the optimal dissemination of information in social networks @inproceedings{farzhalinjovCDC12, author = {M. Fardad and X. Zhang and F. Lin and M. R. Jovanović}, title = {On the optimal dissemination of information in social networks}, booktitle = {Proceedings of the 51th IEEE Conference on Decision and Control}, year = {2012}, pages = {2539-2544}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/conference/2012/FardadZhangLinJovanovicCDC2012.pdf} }
Dynamics of the roll and streak structure in transition and turbulence @inproceedings{fargayioaliejovCTR12, author = {B. F. Farrell and D. F. Gayme and P. J. Ioannou and B. K. Lieu and M. R. Jovanović}, title = {Dynamics of the roll and streak structure in transition and turbulence}, booktitle = {Proceedings of the 2012 Summer Program}, year = {2012}, pages = {43-54} }
The use of the r* heuristic in covariance completion problems @inproceedings{gruzarjovranCDC16, author = {C. Grussler and A. Zare and M. R. Jovanović and A. Rantzer}, title = {The use of the r* heuristic in covariance completion problems}, booktitle = {Proceedings of the 55th IEEE Conference on Decision and Control}, year = {2016}, pages = {1978-1983}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/gruzarjovranCDC16.pdf} }
Amplification of localized body forces in channel flows of viscoelastic fluids @article{harjovkumJNNFM18, author = {G. Hariharan and M. R. Jovanović and S. Kumar}, title = {Amplification of localized body forces in channel flows of viscoelastic fluids}, journal = {J. Non-Newtonian Fluid Mech.}, year = {2018}, volume = {260}, pages = {40-53}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/harjovkumJNNFM18.pdf} }
Spatio-temporal impulse responses in channel flow of viscoelastic fluids @inproceedings{harjovkumACC18, author = {G. Hariharan and M. R. Jovanović and S. Kumar}, title = {Spatio-temporal impulse responses in channel flow of viscoelastic fluids}, booktitle = {Proceedings of the 2018 American Control Conference}, year = {2018}, pages = {2857-2862}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/harjovkumACC18.pdf} }
Analysis, design, and optimization of large-scale networks of dynamical systems @phdthesis{sepideh-phd19, author = {S. Hassan-Moghaddam}, title = {Analysis, design, and optimization of large-scale networks of dynamical systems}, institution = {University of Southern California}, school = {University of Southern California}, year = {2019}, pdf = {/viterbi-web.usc.edu/~mihailo/theses/SepidehHassanMoghaddam-PhD.pdf} }
Topology identification of undirected consensus networks via sparse inverse covariance estimation @inproceedings{mogdhijovCDC16, author = {S. Hassan-Moghaddam and N. K. Dhingra and M. R. Jovanović}, title = {Topology identification of undirected consensus networks via sparse inverse covariance estimation}, booktitle = {Proceedings of the 55th IEEE Conference on Decision and Control}, year = {2016}, pages = {4624-4629}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mogdhijovCDC16.pdf} }
Global exponential stability of the Douglas-Rachford splitting dynamics @inproceedings{mogjovIFAC20, author = {S. Hassan-Moghaddam and M. R. Jovanović}, title = {Global exponential stability of the Douglas-Rachford splitting dynamics}, booktitle = {Preprints of the 21th IFAC World Congress}, year = {2020}, note = {to appear} }
Proximal gradient flow and Douglas-Rachford splitting dynamics: global exponential stability via integral quadratic constraints @article{mogjovAUT19, author = {S. Hassan-Moghaddam and M. R. Jovanović}, title = {Proximal gradient flow and Douglas-Rachford splitting dynamics: global exponential stability via integral quadratic constraints}, journal = {Automatica}, year = {2019}, note = {submitted; also arXiv:1908.09043}, pdf = {/arxiv.org/abs/1908.09043} }
Distributed proximal augmented Lagrangian method for nonsmooth composite optimization @inproceedings{mogjovACC18, author = {S. Hassan-Moghaddam and M. R. Jovanović}, title = {Distributed proximal augmented Lagrangian method for nonsmooth composite optimization}, booktitle = {Proceedings of the 2018 American Control Conference}, year = {2018}, pages = {2047-2052}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mogjovACC18.pdf} }
On the exponential convergence rate of proximal gradient flow algorithms @inproceedings{mogjovCDC18a, author = {S. Hassan-Moghaddam and M. R. Jovanović}, title = {On the exponential convergence rate of proximal gradient flow algorithms}, booktitle = {Proceedings of the 57th IEEE Conference on Decision and Control}, year = {2018}, pages = {4246-4251}, note = {(Invited paper)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mogjovCDC18a.pdf} }
Topology design for stochastically-forced consensus networks @article{mogjovTCNS18, author = {S. Hassan-Moghaddam and M. R. Jovanović}, title = {Topology design for stochastically-forced consensus networks}, journal = {IEEE Trans. Control Netw. Syst.}, year = {2018}, volume = {5}, number = {3}, pages = {1075-1086}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mogjovTCNS18.pdf} }
Topology identification via growing a Chow-Liu tree network @inproceedings{mogjovCDC18b, author = {S. Hassan-Moghaddam and M. R. Jovanović}, title = {Topology identification via growing a Chow-Liu tree network}, booktitle = {Proceedings of the 57th IEEE Conference on Decision and Control}, year = {2018}, pages = {5421-5426}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mogjovCDC18b.pdf} }
Distributed design of optimal structured feedback gains @inproceedings{mogjovCDC17, author = {S. Hassan-Moghaddam and M. R. Jovanović}, title = {Distributed design of optimal structured feedback gains}, booktitle = {Proceedings of the 56th IEEE Conference on Decision and Control}, year = {2017}, pages = {6586-6591}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mogjovCDC17.pdf} }
Customized algorithms for growing connected resistive networks @inproceedings{mogjovNOL16, author = {S. Hassan-Moghaddam and M. R. Jovanović}, title = {Customized algorithms for growing connected resistive networks}, booktitle = {Proceedings of the 10th IFAC Symposium on Nonlinear Control Systems}, year = {2016}, pages = {986-991}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mogjovNOL16.pdf} }
An interior point method for growing connected resistive networks @inproceedings{mogjovACC15, author = {S. Hassan-Moghaddam and M. R. Jovanović}, title = {An interior point method for growing connected resistive networks}, booktitle = {Proceedings of the 2015 American Control Conference}, year = {2015}, pages = {1223-1228}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mogjovACC15.pdf} }
Data-driven proximal algorithms for the design of structured optimal feedback gains @inproceedings{mogjovmeyACC19, author = {S. Hassan-Moghaddam and M. R. Jovanović and S. Meyn}, title = {Data-driven proximal algorithms for the design of structured optimal feedback gains}, booktitle = {Proceedings of the 2019 American Control Conference}, year = {2019}, pages = {5846-5850}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mogjovmeyACC19.pdf} }
Edge addition in directed consensus networks @inproceedings{mogwujovACC17, author = {S. Hassan-Moghaddam and X. Wu and M. R. Jovanović}, title = {Edge addition in directed consensus networks}, booktitle = {Proceedings of the 2017 American Control Conference}, year = {2017}, pages = {5592-5597}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mogwujovACC17.pdf} }
Sensitivity analysis for the control of oblique shock wavelaminar boundary layer interactions at Mach 5.92/ @inproceedings{hildwiniccanjovAIAA17, author = {N. Hildebrand and A. Dwivedi and J. W. Nichols and G. V. Candler and M. R. Jovanović}, title = {Sensitivity analysis for the control of oblique shock wave/laminar boundary layer interactions at Mach 5.92}, booktitle = {Proceedings of the 47th AIAA Fluid Dynamics Conference}, year = {2017}, pages = {4312 (14 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/hildwiniccanjovAIAA17.pdf} }
Simulation and stability analysis of oblique shock waveboundary layer interactions at Mach 5.92/ @article{hildwinicjovcanPRF18, author = {N. Hildebrand and A. Dwivedi and J. W. Nichols and M. R. Jovanović and G. V. Candler}, title = {Simulation and stability analysis of oblique shock wave/boundary layer interactions at Mach 5.92}, journal = {Phys. Rev. Fluids}, year = {2018}, volume = {3}, number = {1}, pages = {013906 (23 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/hildwinicjovcanPRF18.pdf} }
Instabilities in laminar shock boundary layer interactions @inproceedings{hildwisidnicjovcanIUTAM19, author = {N. Hildebrand and A. Dwivedi and G. S. Sidharth and J. W. Nichols and M. R. Jovanović and G. V. Candler}, title = {Instabilities in laminar shock boundary layer interactions}, booktitle = {Proceedings of the 2019 IUTAM Symposium on Laminar-Turbulent Transition}, year = {2019}, note = {to appear} }
Transient growth in oblique shock wavelaminar boundary layer interactions at Mach 5.92/ @inproceedings{hilniccanjovAIAA18, author = {N. Hildebrand and J. W. Nichols and G. V. Candler and M. R. Jovanović}, title = {Transient growth in oblique shock wave/laminar boundary layer interactions at Mach 5.92}, booktitle = {Proceedings of the 48th AIAA Fluid Dynamics Conference}, year = {2018}, pages = {3221 (17 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/hilniccanjovAIAA18.pdf} }
Transient growth analysis of oblique shock-waveboundary-layer interactions in a hypersonic flow/ @article{hilnicjovcanPRF19, author = {N. Hildebrand and J. W. Nichols and M. R. Jovanović and G. V. Candler}, title = {Transient growth analysis of oblique shock-wave/boundary-layer interactions in a hypersonic flow}, journal = {Phys. Rev. Fluids}, year = {2019}, note = {submitted; also arXiv:1901.09132}, pdf = {/arxiv.org/abs/1901.09132} }
Frequency responses of streamwise-constant perturbations in channel flows of Oldroyd-B fluids @article{hodjovkumJFM09, author = {N. Hoda and M. R. Jovanović and S. Kumar}, title = {Frequency responses of streamwise-constant perturbations in channel flows of Oldroyd-B fluids}, journal = {J. Fluid Mech.}, year = {2009}, volume = {625}, pages = {411-434}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jfm09.pdf} }
Energy amplification in channel flows of viscoelastic fluids @article{hodjovkumJFM08, author = {N. Hoda and M. R. Jovanović and S. Kumar}, title = {Energy amplification in channel flows of viscoelastic fluids}, journal = {J. Fluid Mech.}, year = {2008}, volume = {601}, pages = {407-424}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jfm08.pdf} }
Input-output analysis of the 2D3C model in channel flows of viscoelastic fluids/ @inproceedings{hodjovkumCDC08, author = {N. Hoda and M. R. Jovanović and S. Kumar}, title = {Input-output analysis of the 2D/3C model in channel flows of viscoelastic fluids}, booktitle = {Proceedings of the 47th IEEE Conference on Decision and Control}, year = {2008}, pages = {841-846}, note = {(Invited paper)} }
Input-output analysis of heated axisymmetric turbulent jets @inproceedings{jeunicjovAIAA16, author = {J. Jeun and J. W. Nichols and M. R. Jovanović}, title = {Input-output analysis of heated axisymmetric turbulent jets}, booktitle = {Proceedings of the 22nd AIAA/CEAS Aeroacoustics Conference}, year = {2016}, pages = {2934 (13 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jeunicjovAIAA16.pdf} }
Input-output analysis of high-speed axisymmetric isothermal jet noise @article{jeunicjovPOF16, author = {J. Jeun and J. W. Nichols and M. R. Jovanović}, title = {Input-output analysis of high-speed axisymmetric isothermal jet noise}, journal = {Phys. Fluids}, year = {2016}, volume = {28}, number = {4}, pages = {047101 (20 pages)}, note = {(Editor's Pick)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jeunicjovPOF16.pdf} }
From bypass transition to flow control and data-driven turbulence modeling: An input-output viewpoint @article{jovARFM20, author = {M. R. Jovanović}, title = {From bypass transition to flow control and data-driven turbulence modeling: An input-output viewpoint}, journal = {Annu. Rev. Fluid Mech.}, year = {2020}, note = {submitted; also arXiv:2003.10104}, pdf = {/arxiv.org/abs/2003.10104} }
Vehicular Chains @incollection{jovEC14, author = {M. R. Jovanović}, title = {Vehicular Chains}, booktitle = {Encyclopedia of Systems and Control}, publisher = {Springer-Verlag London}, year = {2014}, pages = {1-10}, note = {doi:10.1007/978-1-4471-5102-921-1}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jovESC14.pdf} }
On the optimality of localized distributed controllers @article{jovIO10, author = {M. R. Jovanović}, title = {On the optimality of localized distributed controllers}, journal = {Int. J. Systems, Control and Communications}, year = {2010}, volume = {2}, number = {1/2/3}, pages = {82-99}, note = {Special issue on Information Processing and Decision Making in Distributed Control Systems}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jovIO10.pdf} }
Turbulence suppression in channel flows by small amplitude transverse wall oscillations @article{jovPOF08, author = {M. R. Jovanović}, title = {Turbulence suppression in channel flows by small amplitude transverse wall oscillations}, journal = {Phys. Fluids}, year = {2008}, volume = {20}, number = {1}, pages = {014101 (11 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/pof08.pdf} }
H_2 norm of linear time-periodic systems: a perturbation analysis @inproceedings{jovACC06h2pert, author = {M. R. Jovanović}, title = {H_2 norm of linear time-periodic systems: a perturbation analysis}, booktitle = {Proceedings of the 2006 American Control Conference}, year = {2006}, pages = {1452-1457} }
Turbulence suppression in channel flows by small amplitude transverse wall oscillations @inproceedings{jovACC06two, author = {M. R. Jovanović}, title = {Turbulence suppression in channel flows by small amplitude transverse wall oscillations}, booktitle = {Proceedings of the 2006 American Control Conference}, year = {2006}, pages = {1161-1166}, note = {(Invited paper)} }
On the optimality of localized distributed controllers @inproceedings{jovACC05, author = {M. R. Jovanović}, title = {On the optimality of localized distributed controllers}, booktitle = {Proceedings of the 2005 American Control Conference}, year = {2005}, pages = {4583-4588}, note = {(Invited paper)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/acc05io.pdf} }
Modeling, analysis, and control of spatially distributed systems @phdthesis{mj-phd04, author = {M. R. Jovanović}, title = {Modeling, analysis, and control of spatially distributed systems}, institution = {University of California, Santa Barbara}, school = {University of California, Santa Barbara}, year = {2004}, pdf = {/viterbi-web.usc.edu/~mihailo/theses/mj-thesis.pdf} }
Nonlinear control of an electrohydraulic velocity servosystem @inproceedings{jovACC02, author = {M. R. Jovanović}, title = {Nonlinear control of an electrohydraulic velocity servosystem}, booktitle = {Proceedings of the 2002 American Control Conference}, year = {2002}, pages = {588-593}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/acc02.pdf} }
The jth order practical tracking @inproceedings{jov98, author = {M. R. Jovanović}, title = {The jth order practical tracking}, booktitle = {Proceedings of the 6th International Conference on Systems, Automatic Control and Measurements}, year = {1998} }
A passivity-based approach to stability of spatially distributed systems with a cyclic interconnection structure @article{jovarcsonTAC08, author = {M. R. Jovanović and M. Arcak and E. D. Sontag}, title = {A passivity-based approach to stability of spatially distributed systems with a cyclic interconnection structure}, journal = {IEEE Trans. Automat. Control: Special Issue on Systems Biology}, year = {2008}, volume = {53}, pages = {75-86}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/tac08secant.pdf} }
Remarks on the stability of spatially distributed systems with a cyclic interconnection structure @inproceedings{jovarcsonACC07, author = {M. R. Jovanović and M. Arcak and E. D. Sontag}, title = {Remarks on the stability of spatially distributed systems with a cyclic interconnection structure}, booktitle = {Proceedings of the 2007 American Control Conference}, year = {2007}, pages = {2696-2701} }
Architecture induced by distributed backstepping design @article{jovbamTAC07arc, author = {M. R. Jovanović and B. Bamieh}, title = {Architecture induced by distributed backstepping design}, journal = {IEEE Trans. Automat. Control}, year = {2007}, volume = {52}, number = {1}, pages = {108-113}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/tac07arc.pdf} }
A formula for frequency responses of distributed systems with one spatial variable @article{jovbamSCL06, author = {M. R. Jovanović and B. Bamieh}, title = {A formula for frequency responses of distributed systems with one spatial variable}, journal = {Syst. Control Lett.}, year = {2006}, volume = {55}, number = {1}, pages = {27-37}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/scl06.pdf} }
Componentwise energy amplification in channel flows @article{jovbamJFM05, author = {M. R. Jovanović and B. Bamieh}, title = {Componentwise energy amplification in channel flows}, journal = {J. Fluid Mech.}, year = {2005}, volume = {534}, pages = {145-183}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jfm05.pdf} }
Lyapunov-based distributed control of systems on lattices @article{jovbamTAC05lattice, author = {M. R. Jovanović and B. Bamieh}, title = {Lyapunov-based distributed control of systems on lattices}, journal = {IEEE Trans. Automat. Control}, year = {2005}, volume = {50}, number = {4}, pages = {422-433}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/tac05lattice.pdf} }
On the ill-posedness of certain vehicular platoon control problems @article{jovbamTAC05platoons, author = {M. R. Jovanović and B. Bamieh}, title = {On the ill-posedness of certain vehicular platoon control problems}, journal = {IEEE Trans. Automat. Control}, year = {2005}, volume = {50}, number = {9}, pages = {1307-1321}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/tac05platoons.pdf} }
Architecture induced by distributed backstepping design @inproceedings{jovbamCDC04arc, author = {M. R. Jovanović and B. Bamieh}, title = {Architecture induced by distributed backstepping design}, booktitle = {Proceedings of the 43rd IEEE Conference on Decision and Control}, year = {2004}, pages = {3774-3779}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/cdc04arc.pdf} }
On the ill-posedness of certain vehicular platoon control problems @inproceedings{jovbamCDC04platoons, author = {M. R. Jovanović and B. Bamieh}, title = {On the ill-posedness of certain vehicular platoon control problems}, booktitle = {Proceedings of the 43rd IEEE Conference on Decision and Control}, year = {2004}, pages = {3780-3785}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/cdc04platoons.pdf} }
Unstable modes versus non-normal modes in supercritical channel flows @inproceedings{jovbamACC04, author = {M. R. Jovanović and B. Bamieh}, title = {Unstable modes versus non-normal modes in supercritical channel flows}, booktitle = {Proceedings of the 2004 American Control Conference}, year = {2004}, pages = {2245-2250}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/acc04fh.pdf} }
Exact computation of frequency responses for a class of infinite dimensional systems @inproceedings{jovbamCDC03fr-exact, author = {M. R. Jovanović and B. Bamieh}, title = {Exact computation of frequency responses for a class of infinite dimensional systems}, booktitle = {Proceedings of the 42nd IEEE Conference on Decision and Control}, year = {2003}, pages = {1339-1344}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/cdc03fr-exact.pdf} }
Frequency domain analysis of the linearized Navier-Stokes equations @inproceedings{jovbamACC03fr-lnse, author = {M. R. Jovanović and B. Bamieh}, title = {Frequency domain analysis of the linearized Navier-Stokes equations}, booktitle = {Proceedings of the 2003 American Control Conference}, year = {2003}, pages = {3190-3195}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/acc03fr-lnse.pdf} }
Lyapunov-based output-feedback distributed control of systems on lattices @inproceedings{jovbamCDC03lattice, author = {M. R. Jovanović and B. Bamieh}, title = {Lyapunov-based output-feedback distributed control of systems on lattices}, booktitle = {Proceedings of the 42nd IEEE Conference on Decision and Control}, year = {2003}, pages = {1333-1338}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/cdc03lattice-out.pdf} }
Lyapunov-based state-feedback distributed control of systems on lattices @inproceedings{jovbamACC03lattice, author = {M. R. Jovanović and B. Bamieh}, title = {Lyapunov-based state-feedback distributed control of systems on lattices}, booktitle = {Proceedings of the 2003 American Control Conference}, year = {2003}, pages = {101-106}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/acc03lattice-state.pdf} }
Modelling flow statistics using the linearized Navier-Stokes equations @inproceedings{jovbamCDC01, author = {M. R. Jovanović and B. Bamieh}, title = {Modelling flow statistics using the linearized Navier-Stokes equations}, booktitle = {Proceedings of the 40th IEEE Conference on Decision and Control}, year = {2001}, pages = {4944-4949}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/cdc01.pdf} }
The spatio-temporal impulse response of the linearized Navier-Stokes equations @inproceedings{jovbamACC01, author = {M. R. Jovanović and B. Bamieh}, title = {The spatio-temporal impulse response of the linearized Navier-Stokes equations}, booktitle = {Proceedings of the 2001 American Control Conference}, year = {2001}, pages = {1948-1953}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/acc01.pdf} }
Parametric resonance in spatially distributed systems @inproceedings{jovbamgreACC03, author = {M. R. Jovanović and B. Bamieh and M. Grebeck}, title = {Parametric resonance in spatially distributed systems}, booktitle = {Proceedings of the 2003 American Control Conference}, year = {2003}, pages = {119-124}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/acc03periodic.pdf} }
Stability of linear singular systems on finite time interval under perturbing forces @inproceedings{jovdeb96, author = {M. R. Jovanović and D. Debeljković}, title = {Stability of linear singular systems on finite time interval under perturbing forces}, booktitle = {Proceedings of the 40th ETRAN Conference}, year = {1996}, volume = {1}, pages = {451-453} }
Controller architectures: tradeoffs between performance and structure @article{jovdhiEJC16, author = {M. R. Jovanović and N. K. Dhingra}, title = {Controller architectures: tradeoffs between performance and structure}, journal = {Eur. J. Control}, year = {2016}, volume = {30}, pages = {76-91}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jovdhiEJC16.pdf} }
H_2 norm of linear time-periodic systems: a perturbation analysis @article{jovfarAUT08, author = {M. R. Jovanović and M. Fardad}, title = {H_2 norm of linear time-periodic systems: a perturbation analysis}, journal = {Automatica}, year = {2008}, volume = {44}, number = {8}, pages = {2090-2098}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/aut08h2pert.pdf} }
On the peaking phenomenon in the control of vehicular platoons @article{jovfowbamdan08, author = {M. R. Jovanović and J. M. Fowler and B. Bamieh and R. D'Andrea}, title = {On the peaking phenomenon in the control of vehicular platoons}, journal = {Syst. Control Lett.}, year = {2008}, volume = {57}, number = {7}, pages = {528-537}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/scl08peaking.pdf} }
On avoiding saturation in the control of vehicular platoons @inproceedings{jovfowbamdanACC04, author = {M. R. Jovanović and J. M. Fowler and B. Bamieh and R. D'Andrea}, title = {On avoiding saturation in the control of vehicular platoons}, booktitle = {Proceedings of the 2004 American Control Conference}, year = {2004}, pages = {2257-2262}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/acc04peaking.pdf} }
Nonmodal amplification of stochastic disturbances in strongly elastic channel flows @article{jovkumJNNFM11, author = {M. R. Jovanović and S. Kumar}, title = {Nonmodal amplification of stochastic disturbances in strongly elastic channel flows}, journal = {J. Non-Newtonian Fluid Mech.}, year = {2011}, volume = {166}, number = {14-15}, pages = {755-778}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jovkumJNNFM11.pdf} }
Transient growth without inertia @article{jovkumPOF10, author = {M. R. Jovanović and S. Kumar}, title = {Transient growth without inertia}, journal = {Phys. Fluids}, year = {2010}, volume = {22}, number = {2}, pages = {023101 (19 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jovkumPOF10.pdf} }
Transient response of velocity fluctuations in inertialess channel flows of viscoelastic fluids @inproceedings{jovkumACC10, author = {M. R. Jovanović and S. Kumar}, title = {Transient response of velocity fluctuations in inertialess channel flows of viscoelastic fluids}, booktitle = {Proceedings of the 2010 American Control Conference}, year = {2010}, pages = {5682-5687}, note = {(Invited paper)} }
Variance amplification in channel flows of strongly elastic polymer solutions @inproceedings{jovkumACC09, author = {M. R. Jovanović and S. Kumar}, title = {Variance amplification in channel flows of strongly elastic polymer solutions}, booktitle = {Proceedings of the 2009 American Control Conference}, year = {2009}, pages = {842-847}, note = {(Invited paper)} }
Sparse quadratic regulator @inproceedings{jovlinECC13, author = {M. R. Jovanović and F. Lin}, title = {Sparse quadratic regulator}, booktitle = {Proceedings of the 12th European Control Conference}, year = {2013}, pages = {1047-1052}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jovlinECC13.pdf} }
Turbulence suppression in channel flows by means of a streamwise traveling wave @inproceedings{jovmoayouCTR06, author = {M. R. Jovanović and R. Moarref and D. You}, title = {Turbulence suppression in channel flows by means of a streamwise traveling wave}, booktitle = {Proceedings of the 2006 Summer Program}, year = {2006}, pages = {481-494} }
Sparsity-promoting dynamic mode decomposition @article{jovschnicPOF14, author = {M. R. Jovanović and P. J. Schmid and J. W. Nichols}, title = {Sparsity-promoting dynamic mode decomposition}, journal = {Phys. Fluids}, year = {2014}, volume = {26}, number = {2}, pages = {024103 (22 pages)}, note = {(Editor's Pick)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/jovschnicPOF14.pdf} }
Low-rank and sparse dynamic mode decomposition @inproceedings{jovschnicCTR12, author = {M. R. Jovanović and P. J. Schmid and J. W. Nichols}, title = {Low-rank and sparse dynamic mode decomposition}, booktitle = {Center for Turbulence Research Annual Research Briefs}, year = {2012}, pages = {139-152} }
Practical tracking of a hydraulic cylinder and an axial piston hydraulic motor @inproceedings{lazjovris98, author = {D. V. Lazić and M. R. Jovanović and M. R. Ristanović}, title = {Practical tracking of a hydraulic cylinder and an axial piston hydraulic motor}, booktitle = {Proceedings of Bath Workshop on Power Transmission and Motion Control}, year = {1998}, pages = {331-346} }
Dynamics and control of Newtonian and viscoelastic fluids @phdthesis{binh-phd14, author = {B. K. Lieu}, title = {Dynamics and control of Newtonian and viscoelastic fluids}, institution = {University of Minnesota}, school = {University of Minnesota}, year = {2014}, pdf = {/viterbi-web.usc.edu/~mihailo/theses/BinhLieu-PhD.pdf} }
Computation of frequency responses for linear time-invariant PDEs on a compact interval @article{liejovJCP13, author = {B. K. Lieu and M. R. Jovanović}, title = {Computation of frequency responses for linear time-invariant PDEs on a compact interval}, journal = {J. Comput. Phys.}, year = {2013}, volume = {250}, pages = {246-269}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/liejovJCP13.pdf} }
Model-based analysis of polymer drag reduction in a turbulent channel flow @inproceedings{liejovACC13, author = {B. K. Lieu and M. R. Jovanović}, title = {Model-based analysis of polymer drag reduction in a turbulent channel flow}, booktitle = {Proceedings of the 2013 American Control Conference}, year = {2013}, pages = {485-490}, note = {(Invited paper)} }
Analysis of drag reduction by polymers in a turbulent channel flow @inproceedings{liejovCTR12, author = {B. K. Lieu and M. R. Jovanović}, title = {Analysis of drag reduction by polymers in a turbulent channel flow}, booktitle = {Proceedings of the 2012 Summer Program}, year = {2012}, pages = {65-74} }
Slow-fast decomposition of an inertialess flow of viscoelastic fluids @inproceedings{liejovACC12, author = {B. K. Lieu and M. R. Jovanović}, title = {Slow-fast decomposition of an inertialess flow of viscoelastic fluids}, booktitle = {Proceedings of the 2012 American Control Conference}, year = {2012}, pages = {4369-4374} }
Computation of the frequency responses for distributed systems with one spatial variable @inproceedings{liejovCDC11, author = {B. K. Lieu and M. R. Jovanović}, title = {Computation of the frequency responses for distributed systems with one spatial variable}, booktitle = {Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference}, year = {2011}, pages = {6956-6961} }
Worst-case amplification of disturbances in inertialess flows of viscoelastic fluids @inproceedings{liejovkumIFAC11, author = {B. K. Lieu and M. R. Jovanovic and S. Kumar}, title = {Worst-case amplification of disturbances in inertialess flows of viscoelastic fluids}, booktitle = {Preprints of the 18th IFAC World Congress}, year = {2011}, pages = {14458-14463} }
Worst-case amplification of disturbances in inertialess Couette flow of viscoelastic fluids @article{liejovkumJFM13, author = {B. K. Lieu and M. R. Jovanović and S. Kumar}, title = {Worst-case amplification of disturbances in inertialess Couette flow of viscoelastic fluids}, journal = {J. Fluid Mech.}, year = {2013}, volume = {723}, pages = {232-263}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/liejovkumJFM13.pdf} }
Controlling the onset of turbulence by streamwise traveling waves. Part 2: Direct numerical simulations @article{liemoajovJFM10, author = {B. K. Lieu and R. Moarref and M. R. Jovanović}, title = {Controlling the onset of turbulence by streamwise traveling waves. Part 2: Direct numerical simulations}, journal = {J. Fluid Mech.}, year = {2010}, volume = {663}, pages = {100-119}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/liemoajovJFM10.pdf} }
Preventing transition to turbulence using streamwise traveling waves: direct numerical simulations @inproceedings{liemoajovACC10, author = {B. K. Lieu and R. Moarref and M. R. Jovanović}, title = {Preventing transition to turbulence using streamwise traveling waves: direct numerical simulations}, booktitle = {Proceedings of the 2010 American Control Conference}, year = {2010}, pages = {3335-3340} }
Structure identification and optimal design of large-scale networks of dynamical systems @phdthesis{fu-phd12, author = {F. Lin}, title = {Structure identification and optimal design of large-scale networks of dynamical systems}, institution = {University of Minnesota}, school = {University of Minnesota}, year = {2012}, pdf = {/viterbi-web.usc.edu/~mihailo/theses/FuLin-PhD.pdf} }
Algorithms for leader selection in stochastically forced consensus networks @article{linfarjovTAC14leaderselection, author = {F. Lin and M. Fardad and M. R. Jovanović}, title = {Algorithms for leader selection in stochastically forced consensus networks}, journal = {IEEE Trans. Automat. Control}, year = {2014}, volume = {59}, number = {7}, pages = {1789-1802}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/linfarjovTAC14LeaderSelection.pdf} }
Design of optimal sparse feedback gains via the alternating direction method of multipliers @article{linfarjovTAC13admm, author = {F. Lin and M. Fardad and M. R. Jovanović}, title = {Design of optimal sparse feedback gains via the alternating direction method of multipliers}, journal = {IEEE Trans. Automat. Control}, year = {2013}, volume = {58}, number = {9}, pages = {2426-2431}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/linfarjovTAC13admm.pdf} }
Identification of sparse communication graphs in consensus networks @inproceedings{linfarjovALL12, author = {F. Lin and M. Fardad and M. R. Jovanović}, title = {Identification of sparse communication graphs in consensus networks}, booktitle = {Proceedings of the 50th Annual Allerton Conference on Communication, Control, and Computing}, year = {2012}, pages = {85-89}, note = {(Invited paper)} }
Optimal control of vehicular formations with nearest neighbor interactions @article{linfarjovTAC12platoons, author = {F. Lin and M. Fardad and M. R. Jovanović}, title = {Optimal control of vehicular formations with nearest neighbor interactions}, journal = {IEEE Trans. Automat. Control}, year = {2012}, volume = {57}, number = {9}, pages = {2203-2218}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/linfarjovTAC12platoons.pdf} }
Performance of leader-follower networks in directed trees and lattices @inproceedings{linfarjovCDC12, author = {F. Lin and M. Fardad and M. R. Jovanović}, title = {Performance of leader-follower networks in directed trees and lattices}, booktitle = {Proceedings of the 51th IEEE Conference on Decision and Control}, year = {2012}, pages = {734-739}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/conference/2012/LinFardadJovanovicCDC2012.pdf} }
Sparse feedback synthesis via the alternating direction method of multipliers @inproceedings{linfarjovACC12, author = {F. Lin and M. Fardad and M. R. Jovanović}, title = {Sparse feedback synthesis via the alternating direction method of multipliers}, booktitle = {Proceedings of the 2012 American Control Conference}, year = {2012}, pages = {4765-4770} }
Algorithms for leader selection in large dynamical networks: noise-corrupted leaders @inproceedings{linfarjovCDC11, author = {F. Lin and M. Fardad and M. R. Jovanović}, title = {Algorithms for leader selection in large dynamical networks: noise-corrupted leaders}, booktitle = {Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference}, year = {2011}, pages = {2932-2937}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/linfarjovCDC11.pdf} }
Augmented Lagrangian approach to design of structured optimal state feedback gains @article{linfarjovTAC11al, author = {F. Lin and M. Fardad and M. R. Jovanović}, title = {Augmented Lagrangian approach to design of structured optimal state feedback gains}, journal = {IEEE Trans. Automat. Control}, year = {2011}, volume = {56}, number = {12}, pages = {2923-2929}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/linfarjovTAC11auglag.pdf} }
On the optimal localized feedback design for multi-vehicle systems @inproceedings{linfarjovCDC10, author = {F. Lin and M. Fardad and M. R. Jovanović}, title = {On the optimal localized feedback design for multi-vehicle systems}, booktitle = {Proceedings of the 49th IEEE Conference on Decision and Control}, year = {2010}, pages = {5744-5749} }
On the optimal localized feedback design for vehicular platoons @inproceedings{linfarjovACC10, author = {F. Lin and M. Fardad and M. R. Jovanović}, title = {On the optimal localized feedback design for vehicular platoons}, booktitle = {Proceedings of the 2010 American Control Conference}, year = {2010}, pages = {4622-4627} }
Synthesis of H_2 optimal static structured controllers: primal and dual formulations @inproceedings{linfarjovALL09, author = {F. Lin and M. Fardad and M. R. Jovanović}, title = {Synthesis of H_2 optimal static structured controllers: primal and dual formulations}, booktitle = {Proceedings of the 47th Annual Allerton Conference on Communication, Control, and Computing}, year = {2009}, pages = {340-346}, note = {(Invited paper)} }
Least-squares approximation of structured covariances @article{linjovTAC09, author = {F. Lin and M. R. Jovanović}, title = {Least-squares approximation of structured covariances}, journal = {IEEE Trans. Automat. Control}, year = {2009}, volume = {54}, number = {7}, pages = {1643-1648}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/linjovTAC09.pdf} }
Energy amplification in a parallel Blasius boundary layer flow subject to free-stream turbulence @inproceedings{linjovACC08, author = {F. Lin and M. R. Jovanović}, title = {Energy amplification in a parallel Blasius boundary layer flow subject to free-stream turbulence}, booktitle = {Proceedings of the 2008 American Control Conference}, year = {2008}, pages = {3070-3075} }
On the least-squares approximation of structured covariances @inproceedings{linjovACC07, author = {F. Lin and M. R. Jovanović}, title = {On the least-squares approximation of structured covariances}, booktitle = {Proceedings of the 2007 American Control Conference}, year = {2007}, pages = {2648-2653} }
An ADMM algorithm for matrix completion of partially known state covariances @inproceedings{linjovgeoCDC13, author = {F. Lin and M. R. Jovanović and T. T. Georgiou}, title = {An ADMM algorithm for matrix completion of partially known state covariances}, booktitle = {Proceedings of the 52nd IEEE Conference on Decision and Control}, year = {2013}, pages = {1684-1689} }
Model-based control of transitional and turbulent wall-bounded shear flows @phdthesis{rashad-phd12, author = {R. Moarref}, title = {Model-based control of transitional and turbulent wall-bounded shear flows}, institution = {University of Minnesota}, school = {University of Minnesota}, year = {2012}, pdf = {/viterbi-web.usc.edu/~mihailo/theses/RashadMoarref-PhD.pdf} }
Perturbation analysis of eigenvalues of a class of self-adjoint operators @inproceedings{moafarjovACC08, author = {R. Moarref and M. Fardad and M. R. Jovanović}, title = {Perturbation analysis of eigenvalues of a class of self-adjoint operators}, booktitle = {Proceedings of the 2008 American Control Conference}, year = {2008}, pages = {955-960}, note = {(Invited paper)} }
Model-based design of transverse wall oscillations for turbulent drag reduction @article{moajovJFM12, author = {R. Moarref and M. R. Jovanović}, title = {Model-based design of transverse wall oscillations for turbulent drag reduction}, journal = {J. Fluid Mech.}, year = {2012}, volume = {707}, pages = {205-240}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/moajovJFM12.pdf} }
Turbulent drag reduction by transverse wall oscillations @inproceedings{moajovACC12, author = {R. Moarref and M. R. Jovanović}, title = {Turbulent drag reduction by transverse wall oscillations}, booktitle = {Proceedings of the 2012 American Control Conference}, year = {2012}, pages = {3359-3364} }
Controlling the onset of turbulence by streamwise traveling waves. Part 1: Receptivity analysis @article{moajovJFM10, author = {R. Moarref and M. R. Jovanović}, title = {Controlling the onset of turbulence by streamwise traveling waves. Part 1: Receptivity analysis}, journal = {J. Fluid Mech.}, year = {2010}, volume = {663}, pages = {70-99}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/moajovJFM10.pdf} }
Preventing transition to turbulence using streamwise traveling waves: theoretical analysis @inproceedings{moajovACC10, author = {R. Moarref and M. R. Jovanović}, title = {Preventing transition to turbulence using streamwise traveling waves: theoretical analysis}, booktitle = {Proceedings of the 2010 American Control Conference}, year = {2010}, pages = {3329-3334} }
Remarks on computing the H_2 norm of incompressible fluids using descriptor state-space formulation @inproceedings{moajovACC08, author = {R. Moarref and M. R. Jovanović}, title = {Remarks on computing the H_2 norm of incompressible fluids using descriptor state-space formulation}, booktitle = {Proceedings of the 2008 American Control Conference}, year = {2008}, pages = {3064-3069} }
On using the streamwise traveling waves for variance suppression in channel flows @inproceedings{moajovACC07, author = {R. Moarref and M. R. Jovanović}, title = {On using the streamwise traveling waves for variance suppression in channel flows}, booktitle = {Proceedings of the 2007 American Control Conference}, year = {2007}, pages = {2060-2065}, note = {(Invited paper; Finalist, Best Student Paper Award)} }
Transition control using an array of streamwise vortices @inproceedings{moajovCDC06, author = {R. Moarref and M. R. Jovanović}, title = {Transition control using an array of streamwise vortices}, booktitle = {Proceedings of the 45th IEEE Conference on Decision and Control}, year = {2006}, pages = {107-112}, note = {(Invited paper)} }
A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization @article{moajovtroshamckPOF14, author = {R. Moarref and M. R. Jovanović and J. A. Tropp and A. S. Sharma and B. J. McKeon}, title = {A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization}, journal = {Phys. Fluids}, year = {2014}, volume = {26}, number = {5}, pages = {051701 (7 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/moajovtroshamckPOF14.pdf} }
Spatially-localized optimal control of transition to turbulence @inproceedings{moaliejovACC11, author = {R. Moarref and B. K. Lieu and M. R. Jovanović}, title = {Spatially-localized optimal control of transition to turbulence}, booktitle = {Proceedings of the 2011 American Control Conference}, year = {2011}, pages = {3577-3582} }
Optimal localized control of transitional channel flow @inproceedings{moaliejovCTR10, author = {R. Moarref and B. K. Lieu and M. R. Jovanović}, title = {Optimal localized control of transitional channel flow}, booktitle = {Proceedings of the 2010 Summer Program}, year = {2010}, pages = {107-118} }
Performance of noisy Nesterov's accelerated method for strongly convex optimization problems @inproceedings{mohrazjovACC19, author = {H. Mohammadi and M. Razaviyayn and M. R. Jovanović}, title = {Performance of noisy Nesterov's accelerated method for strongly convex optimization problems}, booktitle = {Proceedings of the 2019 American Control Conference}, year = {2019}, pages = {3426-3431}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mohrazjovACC19.pdf} }
Robustness of accelerated first-order algorithms for strongly convex optimization problems @article{mohrazjovTAC19, author = {H. Mohammadi and M. Razaviyayn and M. R. Jovanović}, title = {Robustness of accelerated first-order algorithms for strongly convex optimization problems}, journal = {IEEE Trans. Automat. Control}, year = {2019}, note = {conditionally accepted; also arXiv:1905.11011}, pdf = {/arxiv.org/abs/1905.11011} }
On the stability of gradient flow dynamics for a rank-one matrix approximation problem @inproceedings{mohrazjovACC18, author = {H. Mohammadi and M. Razaviyayn and M. R. Jovanović}, title = {On the stability of gradient flow dynamics for a rank-one matrix approximation problem}, booktitle = {Proceedings of the 2018 American Control Conference}, year = {2018}, pages = {4533-4538}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mohrazjovACC18.pdf} }
Variance amplification of accelerated first-order algorithms for strongly convex quadratic optimization problems @inproceedings{mohrazjovCDC18, author = {H. Mohammadi and M. Razaviyayn and M. R. Jovanović}, title = {Variance amplification of accelerated first-order algorithms for strongly convex quadratic optimization problems}, booktitle = {Proceedings of the 57th IEEE Conference on Decision and Control}, year = {2018}, pages = {5753-5758}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mohrazjovCDC18.pdf} }
Learning the model-free linear quadratic regulator via random search @inproceedings{mohsoljovL4DC20, author = {H. Mohammadi and M. Soltanolkotabi and M. R. Jovanović}, title = {Learning the model-free linear quadratic regulator via random search}, booktitle = {Proceedings of the 2nd Learning for Dynamics and Control Conference}, year = {2020}, note = {to appear} }
Random search for learning the linear quadratic regulator @inproceedings{mohsoljovACC20, author = {H. Mohammadi and M. Soltanolkotabi and M. R. Jovanović}, title = {Random search for learning the linear quadratic regulator}, booktitle = {Proceedings of the 2020 American Control Conference}, year = {2020}, note = {to appear} }
Convergence and sample complexity of gradient methods for the model-free linear quadratic regulator problem @article{mohzarsoljovTAC19, author = {H. Mohammadi and A. Zare and M. Soltanolkotabi and M. R. Jovanović}, title = {Convergence and sample complexity of gradient methods for the model-free linear quadratic regulator problem}, journal = {IEEE Trans. Automat. Control}, year = {2019}, note = {submitted; also arXiv:1912.11899}, pdf = {/arxiv.org/abs/1912.11899} }
Global exponential convergence of gradient methods over the nonconvex landscape of the linear quadratic regulator @inproceedings{mohzarsoljovCDC19, author = {H. Mohammadi and A. Zare and M. Soltanolkotabi and M. R. Jovanović}, title = {Global exponential convergence of gradient methods over the nonconvex landscape of the linear quadratic regulator}, booktitle = {Proceedings of the 58th IEEE Conference on Decision and Control}, year = {2019}, pages = {7474-7479}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/mohzarsoljovCDC19.pdf} }
Input-output analysis of high-speed jet noise @inproceedings{nicjovCTR14, author = {J. W. Nichols and M. R. Jovanović}, title = {Input-output analysis of high-speed jet noise}, booktitle = {Proceedings of the 2014 Summer Program}, year = {2014}, pages = {251-260}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/nicjovCTR14.pdf} }
On the feasibility of large-scale automated highways @inproceedings{patbamabbjov08, author = {S. Patterson and B. Bamieh and A. E. Abbadi and M. R. Jovanović}, title = {On the feasibility of large-scale automated highways}, booktitle = {First International Workshop on Computational Transportation Science}, year = {2008}, note = {(Invited paper)} }
Design of optimal coupling gains for synchronization of nonlinear oscillators @inproceedings{purwusindhojovCDC15, author = {V. Purba and X. Wu and M. Sinha and S. V. Dhople and M. R. Jovanović}, title = {Design of optimal coupling gains for synchronization of nonlinear oscillators}, booktitle = {Proceedings of the 54th IEEE Conference on Decision and Control}, year = {2015}, pages = {1310-1315}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/purwusindhojovCDC15.pdf} }
Boundary layer receptivity analysis via the algebraic Lyapunov equation @inproceedings{ranzarhacjovAIAA20, author = {W. Ran and A. Zare and M. J. P. Hack and M. R. Jovanović}, title = {Boundary layer receptivity analysis via the algebraic Lyapunov equation}, booktitle = {Proceedings of the 2020 AIAA SciTech Forum and Exposition}, year = {2020}, pages = {0109 (15 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/ranzarhacjovAIAA20.pdf} }
Modeling mode interactions in boundary layer flows via Parabolized Floquet Equations @article{ranzarhacjovPRF19a, author = {W. Ran and A. Zare and M. J. P. Hack and M. R. Jovanović}, title = {Modeling mode interactions in boundary layer flows via Parabolized Floquet Equations}, journal = {Phys. Rev. Fluids}, year = {2019}, volume = {4}, number = {2}, pages = {023901 (22 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/ranzarhacjovPRF19.pdf} }
Relating global and local stochastic receptivity analysis of boundary layer flows @inproceedings{ranzarhacjovACC19, author = {W. Ran and A. Zare and M. J. P. Hack and M. R. Jovanović}, title = {Relating global and local stochastic receptivity analysis of boundary layer flows}, booktitle = {Proceedings of the 2019 American Control Conference}, year = {2019}, pages = {3212-3217}, note = {(Invited paper)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/ranzarhacjovACC19.pdf} }
Stochastic receptivity analysis of boundary layer flow @article{ranzarhacjovPRF19b, author = {W. Ran and A. Zare and M. J. P. Hack and M. R. Jovanović}, title = {Stochastic receptivity analysis of boundary layer flow}, journal = {Phys. Rev. Fluids}, year = {2019}, volume = {4}, number = {9}, pages = {093901 (28 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/ranzarhacjovPRF19b.pdf} }
Low-complexity modeling of mode interactions in boundary layer flows @inproceedings{ranzarhacjovACC18, author = {W. Ran and A. Zare and M. J. P. Hack and M. R. Jovanović}, title = {Low-complexity modeling of mode interactions in boundary layer flows}, booktitle = {Proceedings of the 2018 American Control Conference}, year = {2018}, pages = {134-139}, note = {(Invited paper)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/ranzarhacjovACC18.pdf} }
Low-complexity stochastic modeling of spatially-evolving flows @inproceedings{ranzarhacjovACC17, author = {W. Ran and A. Zare and M. J. P. Hack and M. R. Jovanović}, title = {Low-complexity stochastic modeling of spatially-evolving flows}, booktitle = {Proceedings of the 2017 American Control Conference}, year = {2017}, pages = {3815-3820}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/ranzarhacjovACC17.pdf} }
Low-complexity stochastic modeling of spatially-evolving flows @inproceedings{ranzarhacjovCTR16, author = {W. Ran and A. Zare and M. J. P. Hack and M. R. Jovanović}, title = {Low-complexity stochastic modeling of spatially-evolving flows}, booktitle = {Proceedings of the 2016 Summer Program}, year = {2016}, pages = {285-294}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/ranzarhacjovCTR16.pdf} }
Frequency-response analysis of riblets for turbulent drag reduction @inproceedings{ranzarjovMTNS20, author = {W. Ran and A. Zare and M. R. Jovanović }, title = {Frequency-response analysis of riblets for turbulent drag reduction}, booktitle = {Proceedings of the 24th International Symposium on Mathematical Theory of Network and Systems}, year = {2020}, note = {submitted} }
Model-based design of riblets for turbulent drag reduction @article{ranzarjovJFM20, author = {W. Ran and A. Zare and M. R. Jovanović}, title = {Model-based design of riblets for turbulent drag reduction}, journal = {J. Fluid Mech.}, year = {2020}, note = {submitted; also arXiv:2002.01671}, pdf = {/arxiv.org/abs/2002.01671} }
Drag reduction in turbulent channel flow over spatially periodic surfaces @inproceedings{ranzarjovCDC19, author = {W. Ran and A. Zare and M. R. Jovanović}, title = {Drag reduction in turbulent channel flow over spatially periodic surfaces}, booktitle = {Proceedings of the 58th IEEE Conference on Decision and Control}, year = {2019}, pages = {5918-5923}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/ranzarjovCDC19.pdf} }
The effect of sponge layers on global stability analysis of Blasius boundary layer flow @inproceedings{ranzarnicjovAIAA17, author = {W. Ran and A. Zare and J. W. Nichols and M. R. Jovanović}, title = {The effect of sponge layers on global stability analysis of Blasius boundary layer flow}, booktitle = {Proceedings of the 47th AIAA Fluid Dynamics Conference}, year = {2017}, pages = {3456 (12 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/ranzarnicjovAIAA17.pdf} }
Application of practical straight-line tracking in the process industry @inproceedings{ribjovjov97, author = {Z. B. Ribar and M. R. Jovanović and R. Z. Jovanović}, title = {Application of practical straight-line tracking in the process industry}, booktitle = {Proceedings of the 41th ETRAN Conference}, year = {1997}, volume = {1}, pages = {444-447} }
Application of practical exponential tracking in fluid transportation industry @inproceedings{riblazjov96, author = {Z. B. Ribar and D. V. Lazić and M. R. Jovanović}, title = {Application of practical exponential tracking in fluid transportation industry}, booktitle = {Proceedings of the 14th International Conference on Material Handling and Warehousing}, year = {1996}, pages = {5.65-5.70} }
Transient growth of accelerated first-order methods @inproceedings{sammohjovACC20, author = {S. Samuelson and H. Mohammadi and M. R. Jovanović}, title = {Transient growth of accelerated first-order methods}, booktitle = {Proceedings of the 2020 American Control Conference}, year = {2020}, note = {to appear} }
Dynamic mode decomposition of H-type transition to turbulence @inproceedings{saynicschjovCTR12, author = {T. Sayadi and J. W. Nichols and P. J. Schmid and M. R. Jovanović}, title = {Dynamic mode decomposition of H-type transition to turbulence}, booktitle = {Proceedings of the 2012 Summer Program}, year = {2012}, pages = {5-14} }
Interaction of an oblique shock with a transitional Mach 5.65 boundary layer @inproceedings{shrdwihilnicjovcanAIAA16, author = {P. Sfhrestha and A. Dwivedi and N. Hildebrand and J. W. Nichols and M. R. Jovanović and G. V. Candler}, title = {Interaction of an oblique shock with a transitional Mach 5.65 boundary layer}, booktitle = {Proceedings of the 46th AIAA Fluid Dynamics Conference}, year = {2016}, pages = {3647 (14 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/shrdwihilnicjovcanAIAA16.pdf} }
Synchronization of limit cycle oscillations in diffusively-coupled systems @inproceedings{shaarcjovACC13, author = {S. Y. Shafi and M. Arcak and M. R. Jovanović}, title = {Synchronization of limit cycle oscillations in diffusively-coupled systems}, booktitle = {Proceedings of the 2013 American Control Conference}, year = {2013}, pages = {4874-4879} }
Synchronization of diffusively-coupled limit cycle oscillators @article{shaarcjovpacAUT13, author = {S. Y. Shafi and M. Arcak and M. R. Jovanović and A. Packard}, title = {Synchronization of diffusively-coupled limit cycle oscillators}, journal = {Automatica}, year = {2013}, volume = {49}, number = {12}, pages = {3613-3622}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/shaarcjovpacAUT13.pdf} }
Study of trip-induced hypersonic boundary layer transition @inproceedings{shrnicjovcanAIAA17, author = {P. Shrestha and J. W. Nichols and M. R. Jovanović and G. V. Candler}, title = {Study of trip-induced hypersonic boundary layer transition}, booktitle = {Proceedings of the 47th AIAA Fluid Dynamics Conference}, year = {2017}, pages = {4513 (21 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/shrnicjovcanAIAA17.pdf} }
Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow @article{tholiejovfarioagayPOF14, author = {V. L. Thomas and B. K. Lieu and M. R. Jovanović and B. F. Farrell and P. J. Ioannou and D. F. Gayme}, title = {Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow}, journal = {Phys. Fluids}, year = {2014}, volume = {26}, number = {10}, pages = {105112 (17 pages)}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/tholiejovfarioagayPOF14.pdf} }
Sparsity-promoting optimal control of power networks @phdthesis{xiaofan-phd16, author = {X. Wu}, title = {Sparsity-promoting optimal control of power networks}, institution = {University of Minnesota}, school = {University of Minnesota}, year = {2016}, pdf = {/viterbi-web.usc.edu/~mihailo/theses/XiaofanWu-PhD.pdf} }
Input-output analysis and decentralized optimal control of inter-area oscillations in power systems @article{wudorjovTPS16, author = {X. Wu and F. Dörfler and M. R. Jovanović}, title = {Input-output analysis and decentralized optimal control of inter-area oscillations in power systems}, journal = {IEEE Trans. Power Syst.}, year = {2016}, volume = {31}, number = {3}, pages = {2434-2444}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/wudorjovTPS16.pdf} }
Topology identification and design of distributed integral action in power networks @inproceedings{wudorjovACC16, author = {X. Wu and F. Dörfler and M. R. Jovanović}, title = {Topology identification and design of distributed integral action in power networks}, booktitle = {Proceedings of the 2016 American Control Conference}, year = {2016}, pages = {5921-5926}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/wudorjovACC16.pdf} }
Decentralized optimal control of inter-area oscillations in bulk power systems @inproceedings{wudorjovCDC15, author = {X. Wu and F. Dörfler and M. R. Jovanović}, title = {Decentralized optimal control of inter-area oscillations in bulk power systems}, booktitle = {Proceedings of the 54th IEEE Conference on Decision and Control}, year = {2015}, pages = {5532-5537}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/wudorjovCDC15.pdf} }
Analysis and design trade-offs for power network inter-area oscillations @inproceedings{wudorjovMTNS14, author = {X. Wu and F. Dörfler and M. R. Jovanović}, title = {Analysis and design trade-offs for power network inter-area oscillations}, booktitle = {Proceedings of the 21st International Symposium on Mathematical Theory of Network and Systems}, year = {2014}, pages = {657-663}, note = {(Invited paper)} }
Sparsity-promoting optimal control of systems with symmetries, consensus and synchronization networks @article{wujovSCL17, author = {X. Wu and M. R. Jovanović}, title = {Sparsity-promoting optimal control of systems with symmetries, consensus and synchronization networks}, journal = {Syst. Control Lett.}, year = {2017}, volume = {103}, pages = {1-8}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/wujovSCL17.pdf} }
Sparsity-promoting optimal control of consensus and synchronization networks @inproceedings{wujovACC14, author = {X. Wu and M. R. Jovanović}, title = {Sparsity-promoting optimal control of consensus and synchronization networks}, booktitle = {Proceedings of the 2014 American Control Conference}, year = {2014}, pages = {2948-2953} }
Low-complexity stochastic modeling of wall-bounded shear flows @phdthesis{armin-phd16, author = {A. Zare}, title = {Low-complexity stochastic modeling of wall-bounded shear flows}, institution = {University of Minnesota}, school = {University of Minnesota}, year = {2016}, pdf = {/viterbi-web.usc.edu/~mihailo/theses/ArminZare-PhD.pdf} }
Low-complexity modeling of partially available second-order statistics: theory and an efficient matrix completion algorithm @article{zarchejovgeoTAC17, author = {A. Zare and Y. Chen and M. R. Jovanović and T. T. Georgiou}, title = {Low-complexity modeling of partially available second-order statistics: theory and an efficient matrix completion algorithm}, journal = {IEEE Trans. Automat. Control}, year = {2017}, volume = {62}, number = {3}, pages = {1368-1383}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/zarchejovgeoTAC17.pdf} }
An alternating minimization algorithm for structured covariance completion problems @inproceedings{zarchejovgeoMTNS16, author = {A. Zare and Y. Chen and M. R. Jovanović and T. T. Georgiou}, title = {An alternating minimization algorithm for structured covariance completion problems}, booktitle = {Proceedings of the 22nd International Symposium on Mathematical Theory of Network and Systems}, year = {2016}, pages = {117-119}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/zarchejovgeoMTNS16.pdf} }
Structured covariance completion via proximal algorithms @inproceedings{zardhijovgeoCDC17, author = {A. Zare and N. K. Dhingra and M. R. Jovanović and T. T. Georgiou}, title = {Structured covariance completion via proximal algorithms}, booktitle = {Proceedings of the 56th IEEE Conference on Decision and Control}, year = {2017}, pages = {3775-3780}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/zardhijovgeoCDC17.pdf} }
Stochastic dynamical modeling of turbulent flows @article{zargeojovARC20, author = {A. Zare and T. T. Georgiou and M. R. Jovanović}, title = {Stochastic dynamical modeling of turbulent flows}, journal = {Annu. Rev. Control Robot. Auton. Syst.}, year = {2020}, volume = {3}, pages = {195-219}, note = {doi:10.1146/annurev-control-053018-023843; also arXiv:1908.09487}, pdf = {/arxiv.org/abs/1908.09487} }
Optimal sensor selection via proximal optimization algorithms @inproceedings{zarjovCDC18, author = {A. Zare and M. R. Jovanović}, title = {Optimal sensor selection via proximal optimization algorithms}, booktitle = {Proceedings of the 57th IEEE Conference on Decision and Control}, year = {2018}, pages = {6514-6519}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/zarjovCDC18.pdf} }
Perturbation of system dynamics and the covariance completion problem @inproceedings{zarjovgeoCDC16, author = {A. Zare and M. R. Jovanovic and T. T. Georgiou}, title = {Perturbation of system dynamics and the covariance completion problem}, booktitle = {Proceedings of the 55th IEEE Conference on Decision and Control}, year = {2016}, pages = {7036-7041}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/zarjovgeoCDC16.pdf} }
Colour of turbulence @article{zarjovgeoJFM17, author = {A. Zare and M. R. Jovanović and T. T. Georgiou}, title = {Colour of turbulence}, journal = {J. Fluid Mech.}, year = {2017}, volume = {812}, pages = {636-680}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/zarjovgeoJFM17.pdf} }
Alternating direction optimization algorithms for covariance completion problems @inproceedings{zarjovgeoACC15, author = {A. Zare and M. R. Jovanović and T. T. Georgiou}, title = {Alternating direction optimization algorithms for covariance completion problems}, booktitle = {Proceedings of the 2015 American Control Conference}, year = {2015}, pages = {515-520}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/zarjovgeoACC15.pdf} }
Completion of partially known turbulent flow statistics @inproceedings{zarjovgeoACC14, author = {A. Zare and M. R. Jovanović and T. T. Georgiou}, title = {Completion of partially known turbulent flow statistics}, booktitle = {Proceedings of the 2014 American Control Conference}, year = {2014}, pages = {1680-1685}, note = {(Invited paper; Finalist, Best Student Paper Award)} }
Completion of partially known turbulent flow statistics via convex optimization @inproceedings{zarjovgeoCTR14, author = {A. Zare and M. R. Jovanović and T. T. Georgiou}, title = {Completion of partially known turbulent flow statistics via convex optimization}, booktitle = {Proceedings of the 2014 Summer Program}, year = {2014}, pages = {345-354}, pdf = {/viterbi-web.usc.edu/~mihailo/papers/zarjovgeoCTR14.pdf} }
Turbulent drag reduction by streamwise traveling waves @inproceedings{zarliejovCDC12, author = {A. Zare and B. K. Lieu and M. R. Jovanović}, title = {Turbulent drag reduction by streamwise traveling waves}, booktitle = {Proceedings of the 51th IEEE Conference on Decision and Control}, year = {2012}, pages = {3122-3126} }
Proximal algorithms for large-scale statistical modeling and sensoractuator selection/ @article{zarmohdhigeojovTAC19, author = {A. Zare and H. Mohammadi and N. K. Dhingra and T. T. Georgiou and M. R. Jovanović}, title = {Proximal algorithms for large-scale statistical modeling and sensor/actuator selection}, journal = {IEEE Trans. Automat. Control}, year = {2019}, note = {doi:10.1109/TAC.2019.2948268; also arXiv:1807.01739}, pdf = {/arxiv.org/abs/1807.01739} }
Sparsity-promoting optimal control of spatially-invariant systems @inproceedings{zoldhilinjovACC14, author = {D. M. Zoltowski and N. K. Dhingra and F. Lin and M. R. Jovanović}, title = {Sparsity-promoting optimal control of spatially-invariant systems}, booktitle = {Proceedings of the 2014 American Control Conference}, year = {2014}, pages = {1261-1266} } Basic exampleWe illustrate basic features of SISMatlab using the differential equation, \[ \begin{equation} \left( \mathrm D^{2} \; + \; \dfrac{1}{y^2 + 1} \, \mathrm D \; - \; \epsilon^2 I \right) \phi (y) \; = \; d(y), \label{eq:2} \end{equation} \] with Dirichlet, Neumann, or Robin boundary conditions, \[ \begin{align} \phi (\pm 1) \;& =\; \pm 1, \label{eq:1b} \\[0.1cm] [{\mathrm D} \phi (\cdot)](\pm 1) \;& =\; \pm 2, \label{eq:1c} \\[0.1cm] 4\,[{\mathrm D} \phi (\cdot)](\pm 1) \,+\, 3\,\phi (\pm 1) \;&=\; \pm 3, \label{eq:1d} \end{align} \]
Solving TPBVPs via sisSolvesWe first use function sisSolves to solve Eq. \(\eqref{eq:2}\) with boundary conditions \(\eqref{eq:1b}\), \(\eqref{eq:1c}\), or \(\eqref{eq:1d}\).
Step 1: Problem data
% Set problem data % number of basis functions, differential order, spatial variable, parameters N = 63; % N has to be an odd number m = 2; % order of differential operator y = sety(N); % spatially-independent variable % parameter eps in TPBVP eps = 1; eps2 = eps*eps; Step 2: Operator and input in TPBVP
% Represent operator in TPBVP Delta = cell(m+1,1); % cell array with coefficients Delta{1} = 1.0; Delta{2} = 1./(y.^2 + 1); Delta{3} = -eps2; % Input in physical space d = 1 + y + y.^2; Step 3: Boundary conditions
% Dirichlet BCs bc1 = BCs(2,1); % two constraints on one variable % Identity operator I = cell(1,1); % cell array with coefficients I{1} = 1.0; % Dirichlet BCs at y = \pm 1 bc1.Operator = {I; I}; % boundary operator bc1.Points = [1; -1]; % boundary points bc1.Values = [1; -1]; % BCs at the boundaries ([0; 0] for homogeneous BCs) % Neumann BCs bc2 = BCs(2,1); % two constraints on one variable % 1st derivative operator: 1.0 Dy + 0.0 I Dy = cell(2,1); % cell array with coefficients Dy{1} = 1.0; Dy{2} = 0.0; % Neumann BCs at y = \pm 1 bc2.Operator = {Dy; Dy}; bc2.Points = [1; -1]; bc2.Values = [2; -2]; % Robin BCs bc3 = BCs(2,1); % two constraints on one variable % Operator 4 Dy + 3 I Op = cell(2,1); % cell array with coefficients Op{1} = 4; Op{2} = 3; % Robin BCs at y = \pm 1 bc3.Operator = {Op; Op}; bc3.Points = [1; -1]; bc3.Values = [3; -3]; We now use sisSolves to solve the TPBVP. sisSolves takes five inputs: order of the differential equation \(m\) (Eq. \(\eqref{eq:2}\) is a 2nd order differential equation), the number of basis functions \(N\), the operator to be discretized (cell array in Matlab), input function \(d\), and the boundary conditions. Step 4: Solve TPBVP
% Use sisSolves to solve TPBVP % inputs to sisSolves: differential order m, N, operator, BCs, input forcing d solution1 = sisSolves(m,N,Delta,bc1,d); % Dirichlet BCs solution2 = sisSolves(m,N,Delta,bc2,d); % Neumann BCs solution3 = sisSolves(m,N,Delta,bc3,d); % Robin BCs % Visualize solution for Dirichlet BCs plot(y,solution1); The spectral integration methodIn the spectral integration method, the highest derivative is expressed in the basis of Chebyshev polynomials (of the first kind) and indefinite integration is used to obtain expressions for lower derivatives. In Eq. \(\eqref{eq:2}\), the second derivative of \(\phi (y)\) is expressed as \[ \begin{equation} \mathrm D^2\phi (y) \;=\; \sideset{}{’}\sum_{i \, = \, 0}^{\infty} \phi_i^{(2)} \, T_i(y) \; = \; \mathbf t_y^T \, \boldsymbol \Phi^{(2)}, \label{eq:specInt1} \end{equation} \] where the prime denotes a summation with the first term halved, \(\boldsymbol \Phi^{(2)} = [\,\phi^{(2)}_0\;\; \phi^{(2)}_1\;\; \phi^{(2)}_2 \;\; \cdots \;\; ]^T\) is the infinite vector of spectral coefficients in the basis expansion of \(\mathrm D^2\phi (y)\), and \(\mathbf t_y\) is the vector of Chebyshev polynomials, \[ \mathbf t_y^T \; = \; \left[\,\tfrac{1}{2} T_0(y) \;\; T_1(y) \;\; T_2(y) \;\; \cdots \;\;\; \right]. \] Indefinite integration of Eq. \(\eqref{eq:specInt1}\) yields \[ \begin{equation}\label{eq:specInt2} \begin{array}{rclcl} \mathrm D \phi (y) & \, = \,& \displaystyle \sideset{}{’}\sum_{i \, = \, 0}^{N} \phi_i^{(1)} \, T_i(y) \,+\, c_1 & \, = \,& \mathbf t_y^T \, \boldsymbol \Phi^{(1)}\,+\, c_1, \\[0.15cm] \phi (y) & \, = \,& \displaystyle \sideset{}{’}\sum_{i \, = \, 0}^{N} \phi_i^{(0)} \, T_i(y) \,+\, c_1 y \,+\, \tilde{c}_0 & \, = \,& \mathbf t_y^T \, \boldsymbol \Phi^{(0)}\,+\, c_1 y \,+\, \tilde{c}_0, \end{array} \end{equation} \] where \(\tilde{c}_0\) and \(c_1\) are the integration constants. The spectral coefficients \(\boldsymbol \Phi^{(1)}\) and \(\boldsymbol \Phi^{(0)}\) in the basis expansion of \(\mathrm D \phi (y)\) and \(\phi (y)\) can be expressed in terms of \(\boldsymbol \Phi^{(2)}\) via \[ \begin{equation} \begin{array} \boldsymbol \Phi^{(1)} & = & \mathbf Q \, \boldsymbol \Phi^{(2)}, \\[0.1cm] \boldsymbol \Phi^{(0)} & = & \mathbf Q^2 \, \boldsymbol \Phi^{(2)}, \end{array} \end{equation} \] where the indefinite integration operator \(\mathbf Q\) is given by, \[ \begin{equation}\label{eq:Q} \mathbf Q \; = \; \left[\begin{array}{ccccccc} 0& \tfrac{1}{2} & 0 & \cdots\\ \tfrac{1}{2} & 0 & -\tfrac{1}{2} & 0 &\cdots \\ 0 & \tfrac{1}{4} & 0 & -\tfrac{1}{4} & 0 &\cdots \\ 0 & 0 & \tfrac{1}{6} & 0 & -\tfrac{1}{6} & 0 &\cdots \\ \vdots & \vdots & & \ddots & \ddots & \ddots & \\ \end{array}\right]. \end{equation} \] The first row in Eq. \(\eqref{eq:Q}\) is different from Du (Section 4) and Greengard (Eq. 12), and its derivation is provided in the SISMatlab.pdf. In contrast to these references where the first row of \(\mathbf Q\) is full, our representation of \(\mathbf Q\) in Eq. \(\eqref{eq:Q}\) is given by a banded tri-diagonal matrix. Since \(T_0(y) = 1\) and \(T_1(y) = y\), we let \(c_0 = 2 \tilde{c}_0\) and represent integration constants in the basis expansion of \(\phi (y)\) and \(\mathrm D \phi (y)\) in terms of Chebyshev polynomials to obtain, \[ \begin{align}\label{eq:K} \phi (y) \;&=\; \mathbf t_y^T \, \mathbf Q^2 \, \mathbf \Phi^{(2)} \; + \; \left[\begin{array}{cc} \tfrac{1}{2}T_0(y) & T_1(y)\\ \end{array}\right] \overbrace{\left[\begin{array}{cc} 1 & 0\\ 0 & 1 \end{array}\right]}^{\mathbf K^0} \left[\begin{array}{c} c_0 \\ c_1 \end{array}\right], \\[0.1cm] \label{eq:K1} \mathrm D \phi (y) \;&=\; \mathbf t_y^T \, \mathbf Q^{1} \, \boldsymbol \Phi^{(2)} \; + \; \left[\begin{array}{cc} \tfrac{1}{2}T_0(y) & T_1(y)\\ \end{array}\right] \underbrace{\left[\begin{array}{cc} 0 & 2\\ 0 & 0 \end{array}\right]}_{\mathbf K^1} \left[\begin{array}{c} c_0 \\ c_1 \end{array}\right]. \end{align} \] By introducing the vector of integration constants \(\mathbf c^{(2)} = [\begin{array}{cc} c_0 \! & \! c_1 \end{array}]^T\), we can represent \(\phi\), \(\mathrm D \phi\), and \(\mathrm D^2 \phi\) as \[ \begin{alignat}{5} \phi(y) & \,= \,& \mathbf t_y^T \, ( \mathbf Q^2 \, \mathbf \Phi^{(2)} \, + \, \mathbf R_2 \, \mathbf c^{(2)} ) & \,= \,& \mathbf t_y^T \, \underbrace{\left[\begin{array}{cc} \mathbf Q^2 & \mathbf R_2 \end{array}\right]}_{\mathbf{J}_2}\left[\begin{array}{c}\boldsymbol \Phi^{(2)} \\ \mathbf c^{(2)} \end{array}\right], \label{eq:rndu} \\ \mathrm D \phi (y) & \,= \,& \mathbf t_y^T \, ( \mathbf Q^1 \, \mathbf \Phi^{(2)} \,+ \, \mathbf R_1 \, \mathbf c^{(2)} ) & \,= \,& \mathbf t_y^T \, \underbrace{\left[\begin{array}{cc} \mathbf Q^1 & \mathbf R_1 \end{array}\right]}_{\mathbf J_1}\left[\begin{array}{c}\mathbf \Phi^{(2)} \\ \mathbf c^{(2)} \end{array}\right], \label{eq:rndDu} \\ \mathrm D^2 \phi (y) &\;=\;& \mathbf t_y^T \, ( \mathbf Q^0 \, \mathbf \Phi^{(2)} \,+ \, \mathbf R_0 \, \mathbf c^{(2)} ) &\; = \;& \mathbf t_y^T \, \underbrace{\left[\begin{array}{cc} \mathbf Q^0 & \mathbf R_0 \end{array}\right]}_{\mathbf J_0}\left[\begin{array}{c}\mathbf \Phi^{(2)} \\ \mathbf c^{(2)} \end{array}\right], \label{eq:rndD2u} \end{alignat} \] where \(\mathbf Q^0 = \mathbf I\) is the identity operator, \(\mathbf R_{i}\)'s are matrices with an infinite number of rows and two columns, \[ \mathbf R_{i} \, = \, \left[\begin{array}{c} \mathbf K^{2-i} \\ \mathbf 0\end{array} \right], \qquad i \, = \, 0, 1, 2, \] and \(\mathbf K^2 = \mathbf K\,\mathbf K\) is a \(2 \times 2\) zero matrix. Finally, we utilize the expression for the product of two Chebyshev series (see Olver and Townsend and Du) to account for the nonconstant coefficient \(a(y) = 1/(y^2 + 1)\) in Eq. \(\eqref{eq:2}\). For a function \(a(y)\) in the basis of Chebyshev polynomials, \[ \begin{equation} a(y) \;=\; \sideset{}{’}\sum_{i \, = \, 0}^{\infty}\,a_i \,T_i(y), \end{equation} \] the multiplication operator is given by \[ \begin{equation}\label{eq:M} {\mathbf M}_a \;=\; \dfrac{1}{2} \, \left[\begin{array}{ccccc} a_0 & a_1 & a_2 & a_3 & \cdots\\ a_1 & a_0 & a_1 & a_2 & \ddots\\ a_2 & a_1 & a_0 & a_1 & \ddots\\ a_3 & a_2 & a_1 & a_0 & \ddots\\ \vdots & \ddots & \ddots & \ddots& \ddots \end{array}\right] \;+\; \dfrac{1}{2} \, \left[\begin{array}{ccccc} 0 & 0 & 0 & 0 & \cdots\\ a_1 & a_2 & a_3 & a_4 & \cdots\\ a_2 & a_3 & a_4 & a_5 & \ddots\\ a_3 & a_4 & a_5 & a_6 & \ddots\\ \vdots & \ddots & \ddots & \ddots& \ddots \end{array}\right]. \end{equation} \] Thus, in the basis of Chebyshev polynomials, we can express the differential equation \(\eqref{eq:2}\) as, \[ \begin{equation} \label{eq:rndDiff} \mathbf t_y^T \left( \mathbf J_0 \,+\, {\mathbf M}_a\, \mathbf J_1\, - \, \epsilon^2 \mathbf J_2 \right) \left[\begin{array}{c} \boldsymbol \Phi^{(2)} \\ \mathbf c^{(2)} \end{array}\right] \;=\; \mathbf t_y^T \, \mathbf d, \end{equation} \] where \(\mathbf d\) is the vector of spectral coefficients associated with the input \(d (y)\) in Eq. \(\eqref{eq:2}\). Furthermore, we can use Eq. \(\eqref{eq:rndu}\) to write the Dirichlet boundary conditions in Eq. \(\eqref{eq:1b}\) as \[ \begin{align} \begin{split} \mathbf t_{\pm 1}^T \, \mathbf J_2 \left[\begin{array}{c}\boldsymbol \Phi^{(2)} \\ \mathbf c^{(2)} \end{array}\right] \;=\; \pm 1, \end{split}\label{eq:rndDir} \end{align} \] Eq. \(\eqref{eq:rndDu}\) to express the Neumann boundary conditions in Eq. \(\eqref{eq:1c}\) as \[ \begin{align} \begin{split} \mathbf t_{\pm 1}^T \, \mathbf J_1 \left[\begin{array}{c}\boldsymbol \Phi^{(2)} \\ \mathbf c^{(2)} \end{array}\right] \;=\; \pm 2, \end{split}\label{eq:rndNeu} \end{align} \] and Eqs. \(\eqref{eq:rndu}\) and \(\eqref{eq:rndDu}\) to represent the Robin boudary conditions in Eq. \(\eqref{eq:1d}\) as \[ \begin{align} \begin{split} \mathbf t_{\pm 1}^T \,( 4\,\mathbf J_1 \,+ \, 3\,\mathbf J_2 ) \left[\begin{array}{c}\boldsymbol \Phi^{(2)} \\ \mathbf c^{(2)} \end{array}\right] \;=\; \pm 3. \end{split}\label{eq:rndRob} \end{align} \] Combining \(\eqref{eq:rndDiff}\) and \(\eqref{eq:rndDir}\) allows us to represent Eq. \(\eqref{eq:2}\) with Dirichlet boundary conditions Eq. \(\eqref{eq:1b}\) in the basis of Chebyshev polynomials as \[ \begin{equation}\label{eq:rndInfinite} \left[\begin{array}{ccc} \mathbf J_0 \,+\, {\mathbf M}_a \, \mathbf J_1\, - \, \epsilon^2 \mathbf J_2 \\[0.1cm] \mathbf t_{+1}^T \, \mathbf J_2 \\[0.15cm] \mathbf t_{-1}^T \, \mathbf J_2 \end{array}\right]\left[\begin{array}{c} \boldsymbol \Phi^{(2)} \\ \mathbf c^{(2)} \end{array}\right] \;=\; \left[\begin{array}{c} \mathbf d\\ +1\\ -1 \end{array}\right]. \end{equation} \] Similarly, the problem with Neumann and Robin boundary conditions can be solved by replacing the last two rows in Eq. \(\eqref{eq:rndInfinite}\) with Eqs. \(\eqref{eq:rndNeu}\) and \(\eqref{eq:rndRob}\) respectively. Finally, we use the projection operator (Olver and Townsend, Section 2.4) to obtain a finite-dimensional approximation of Eq. \(\eqref{eq:rndInfinite}\) by truncating the infinite vector of spectral coefficients \(\boldsymbol \Phi^{(2)}\) to a vector \(\hat{\boldsymbol \Phi}^{(2)}\) with \(N + 1\) components; see SISMatlab.pdf for details. Operator representation via Discretize and BcMatWe next use functions Discretize and BcMat to obtain the finite-dimensional representation of Eq. \(\eqref{eq:2}\) and to specify boundary conditions, respectively.
Step 1: Problem data
% Set problem data % number of basis functions, differential order, spatial variable, parameters N = 63; % N has to be an odd number m = 2; % order of differential operator y = sety(N); % spatially-independent variable % parameter eps in TPBVP eps = 1; eps2 = eps*eps; We now use Discretize to represent the operator \(\Delta = \mathrm D^{2} + (1/(y^2 + 1))\, \mathrm D - \epsilon^2 I\) in Eq. \(\eqref{eq:2}\). Discretize takes three inputs: order of the differential equation \(m\) (Eq. \(\eqref{eq:2}\) is a 2nd order differential equation), the number of basis functions \(N\), and the operator to be discretized (cell array in Matlab). Step 2: Operator in TPBVP
% Represent operator in TPBVP Delta = cell(m+1,1); % cell array with coefficients Delta{1} = 1.0; Delta{2} = 1./(y.^2 + 1); Delta{3} = -eps2; % Use Discretize to represent Delta Delta = Discretize(m,N,Delta); % inputs: differential order m, N, and the operator We next employ BcMat to specify boundary conditions. BcMat takes four inputs: the order of the differential equation \(m\), the number of basis functions \(N\), the boundary evaluation points (e.g., \(y = \pm 1\) in Eq. \(\eqref{eq:rndDir}\)), and the operator that acts at the boundary (e.g., identity for Dirichlet and first derivative for Neumann BCs).
Step 3: Dirichlet BCs
% Dirichlet BCs % Identity operator I = cell(1,1); % cell array with coefficients I{1} = 1.0; % Dirichlet BCs at y = \pm 1 bcOp = {I; I}; bcPts = [1; -1]; % inputs to BcMat: differential order m, N, boundary points, and boundary operator bc1 = BcMat(m,N,bcPts,bcOp); Implementation of Neumann boundary conditions in Eq. \(\eqref{eq:rndNeu}\). Neumann BCs
% Neumann BCs % 1st derivative operator: 1.0 Dy + 0.0 I Dy = cell(2,1); % cell array with coefficients Dy{1} = 1.0; Dy{2} = 0.0; % Neumann BCs at y = \pm 1 bcOp = {Dy; Dy}; bcPts = [1; -1]; bc2 = BcMat(m,N,bcPts,bcOp); Implementation of Robin boundary conditions in Eq. \(\eqref{eq:rndRob}\). Robin BCs
% Robin BCs % Operator 4 Dy + 3 I Op = cell(2,1); % cell array with coefficients Op{1} = 4; Op{2} = 3; % Robin BCs at y = \pm 1 bcOp = {Op; Op}; bcPts = [1; -1]; bc3 = BcMat(m,N,bcPts,bcOp); Steps 2 and 3 are now combined to obtain a finite-dimensional approximation of the operator in Eq. \(\eqref{eq:rndInfinite}\) for Dirichlet (and similarly for Neumann and Robin) boundary conditions. Step 4: Operator with BCs
% Operator in the equation for spectral coefficients A1 = [Delta; bc1]; % Dirichlet BCs A2 = [Delta; bc2]; % Neumann BCs A3 = [Delta; bc3]; % Robin BCs By setting up the forcing and converting it to the basis of Chebyshev polynomials, i.e., \(d(y) = \mathbf t^T_y \,\mathbf d\), we can obtain the solution. Step 5: Solve TPBVP
% Forcing in physical space d = 1 + y + y.^2; % Forcing in the basis of Chebyshev polynomials d = phys2cheb(d); % Solve differential equation Phi2IntConst1 = A1\[d; 1; -1]; % Dirichlet BCs Phi2IntConst2 = A2\[d; 2; -2]; % Neumann BCs Phi2IntConst3 = A3\[d; 3; -3]; % Robin BCs Vector \(\mathsf{Phi2IntConst}\) contains the first \(N+1\) spectral coefficients \(\hat{\boldsymbol \Phi}^{(2)}\) in the basis representation of \(\mathrm D^2\phi (y)\) in Eq. \(\eqref{eq:specInt1}\) as well as the integration constants \({\mathbf c}^{(2)}\), \[ \mathsf{Phi2IntConst} = \left[\begin{array}{c} \hat{\boldsymbol \Phi}^{(2)} \\ {\mathbf c}^{(2)} \end{array}\right]. \] As illustrated in Eq. \(\eqref{eq:rndu}\), the operator \(\mathbf J_2\) can be utilized to compute the first \(N+1\) spectral coefficients in the basis representation of \(\phi (y)\). Function Matgen provides finite-dimensional approximation of \(\mathbf J_2\). Matgen takes two inputs: the order of the differential equation and \(N\). Step 6: Final solution
% Use Matgen to represent J [~,~,J] = Matgen(m,N); % inputs: the order of the differential equation and N % Compute spectral coefficients in the basis representation of \phi (y) Phi01 = J{end}*Phi2IntConst1; % Dirichlet BCs Phi02 = J{end}*Phi2IntConst2; % Neumann BCs Phi03 = J{end}*Phi2IntConst3; % Robin BCs % Solutions in physical space solution1 = cheb2phys(Phi01); % Dirichlet BCs solution2 = cheb2phys(Phi02); % Neumann BCs solution3 = cheb2phys(Phi03); % Robin BCs % Visualize solution for Dirichlet BCs plot(y,solution1); Elementary discretization matrices via MatgenHerein, we explain how function Matgen can be used to represent matrices \(\mathbf Q\) in Eq. \(\eqref{eq:Q}\), \(\mathbf K\) in Eq. \(\eqref{eq:K}\)-\(\eqref{eq:K1},\) and \(\mathbf J\) in Eq. \(\eqref{eq:rndu}\)-\(\eqref{eq:rndD2u}\). A finite-dimensional representation of the multiplication operator \({\mathbf M}_a\) in Eq. \(\eqref{eq:M}\) that accounts for nonconstant coefficients is obtained using function MultMat. After setting problem data in Step 1, we employ the following steps. Step 2: Operator in TPBVP
% Represent operator in TPBVP % Use Matgen to obtain Q, K, and J [Q,K,J] = Matgen(m,N); % inputs: differential order m and number of basis functions N % Form operator Delta Delta = J{1} + MultMat(1./(y.^2 + 1))*J{2} - eps2*J{3}; Use BcMat to implement boundary conditions. Step 3: Boundary conditions
% Identity operator I = cell(1,1); % cell array with coefficients I{1} = 1.0; % 1st derivative operator: 1.0 Dy + 0.0 I Dy = cell(2,1); % cell array with coefficients Dy{1} = 1.0; Dy{2} = 0.0; % Operator 4 Dy + 3 I Op = cell(2,1); % cell array with coefficients Op{1} = 4; Op{2} = 3; % Implement BCs bc1 = [BcMat(m,N,1,I); BcMat(m,N,-1,I)]; % Dirichlet BCs bc2 = [BcMat(m,N,1,Dy); BcMat(m,N,-1,Dy)]; % Neumann BCs bc3 = [BcMat(m,N,1,Op); BcMat(m,N,-1,Op)]; % Robin BCs Finally, Steps 4, 5, and 6 can be used to compute the corresponding solutions. |