Nonlinearities are unavoidable in most high performance control systems, and this course provides a foundation for treating these systems using the most popular techniques. This course builds on analysis and control design techniques developed in a graduate linear systems course. It will develop further analysis and control design techniques that apply to various types of non-linear systems.

The course begins with a comparison between 2nd order linear and non-linear systems using a phase plane analysis. This provides a survey of various behaviors that can arise in non-linear systems, and sets the stage for analysis and design tools to handle these types of systems.

A foundation for analysis is laid with a discussion of existence and uniqueness of solutions to non-linear ODE's. Then Lyapunov stability is treated in depth, showing how it can be used for analysis as well as control design. Input-Output stability theory is then addressed, including passivity theory and frequency domain analysis/design techniques (absolute stability, describing functions). Examples of their use in feedback systems are presented. Finally, feedback linearization is introduced.

As in the linear systems course (ASEN 5014), key ideas are the focus of the course, with mathematics used to expose these ideas. The required mathematics tools and vocabulary will be covered as needed. The theorem/proof format is avoided in favor of an exposition of useful ``truths'' and a demonstration of the underlying reasons. The course introduces standard viewpoints, methods, and terminology used in the applied and research literature. It is intended as a basis for students pursuing research in the control systems area, and as a resource (set of tools, insights) for the application of control systems in practice.

Required