EE 587 – Nonlinear Control SystemsMihailo Jovanovic,
University of Southern California, Spring 2023
Target audienceGraduate students with interests in control and dynamical systems, robotics, artificial intelligence and machine learning, signal and image processing, communications, computer science and engineering, optimization, power systems, systems biology, and financial engineering. Course descriptionIntroduction and examples of nonlinear systems. Statespace models. Equilibrium points. Linearization. Range of nonlinear phenomena: finite escape time, multiple isolated equilibria, limit cycles, chaos. Bifurcations. Phase portraits. Bendixson and PoincareBendixson criteria. Mathematical background: existence and uniqueness of solutions, continuous dependence on initial conditions and parameters, normed linear spaces, comparison principle, BellmanGronwall Lemma. Lyapunov stability. Lyapunov's direct method. Lyapunov functions. LaSalle's invariance principle. Estimating region of attraction. Control Lyapunov functions. Center manifold theory. Stability of timevarying systems. Gradient algorithm for estimation of unknown parameters. Uniform observability and persistency of excitation. Inputoutput and inputtostate stability. Small gain theorem. Positive real transfer functions. KalmanYakubovichPopov Lemma. Passivity. Circle and Popov criteria for absolute stability. Theory of integral quadratic constraints. Feedback and inputoutput linearization. Relative degree and zero dynamics. Model reference adaptive control. Integrator backstepping. Adaptive backstepping design. Class schedule
Mo/Wed, 10:00  11:50am, Dr. Joseph Medicine Crow Center for International and Public Affairs (CPA) 155 Instructor and Teaching Assistant
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