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Nonlinear Systems and Control
Course Description
This graduate course covers fundamentals of nonlinear systems analysis and
control. It is intended for studenst who have had a graduate course in
linear dynamical systems, but no prior exposure to nonlinear dynamical systems.
The first part of the course will focus on analysis of nonlinear systems, driven
by a number of real-world examples, and some preliminary mathematical background.
The second portion of the course will focus on stability through
Lyapunov techniques and input-output analysis. The third portion of the course
will focus on control of nonlinear systems, through feedback linearization,
sliding mode control, and gain scheduling.
Course Outline and Syllabus
Course syllabus
- Introduction and review: Examples, linearization through Taylor's series.
- Analysis of nonlinear phenomena: Hartman-Grobmann theorem, local stability, multiple equilibria, limit cycles, bifurcations.
- Planar systems: phase plane techniques, Bendixson's theorem, Poincare-Bendixson Theorem.
- Mathematical background: Contraction mapping theorem, homeomorphisms, norms.
- Input-output analysis and stability: Small gain theorem, passivity, describing functions.
- Lyapunov stability theory: Lyapunov stability. Lyapunov functions, asymptotic stability, exponential stability, LaSalle's Theorem, Indirect method.
- Feedback linearization: Input-output linearization, full-state linearization, stabilization, tracking. Zero dynamics, MIMO systems, non-minimum phase systems, singularities.
- Sliding mode control: Sliding surfaces, differential inclusions, solutions in the sense of Filippov.
- Gain scheduling: Controller and scheduling design.
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