Course Overview

This course provides a basic introduction to nonlinear dynamical systems and their control. The first module begins with an overview of nonlinear system models, and types of behaviors that can only arise in nonlinear systems. It then introduces phase portraits for systems with two state variables, states basic existence and uniqueness results for solutions of ordinary differential equations, and concludes with sensitivity equations that allow one to evaluate the sensitivity of the solutions with respect to parameters and initial conditions. The second module introduces Lyapunov stability theory and Lyapunov functions. It proceeds to linearization as a method for determining local stability properties around operating points, and defines the notion of a region of attraction. The third module focuses on feedback control design for nonlinear systems, starting with backstepping as an example of Lyapunov-based feedback design to stabilize an operating point. It continues with input/output linearization for trajectory tracking, by first introducing requisite concepts such as relative degree. The fourth module introduces feedback linearization for stabilization, then proceeds to sliding mode control for stabilization in the presence of model uncertainty. The course will illustrate all concepts with physically-motivated examples, and will point to resources for further study.