Introduction to the theory of systems of coupled, nonlinear, time-varying ordinary differential equations: existence and uniqueness of solutions; continuous dependence on parameters; stability of equilibria and stability analysis techniques; input-to-state stability; input-output stability; nonlinear control design techniques including input-state and input-output feedback linearization, backstepping, and sliding mode control.
Nonlinear systems theory provides a theoretical framework for studying a large class of systems that are not amenable to linear systems techniques. Moreover, nonlinear techniques can strengthen conclusions about the behavior of those systems which are amenable to linear analysis. Nonlinear systems theory also forms the basis for a variety of nonlinear control design methods that can improve closed-loop performance and robustness beyond the capabilities of linear control design methods.
Percentage of Course
|1. Nonlinear System Analysis - Existence and uniqueness of solutions; continuous dependence on parameters; stability of equilibria and analysis techniques.||25%|
|2. Control System Properties - Input-to-state stability, input-output stability, L2gain, small gain theorem||25%|
|3. Control Design Techniques.||%|
|a. Input-state linearization||20%|
|b. Input-output linearization||10%|
|c. Sliding mode control, backstepping, advanced topics||20%|