Nonlinear Systems Analysis and Control

Description

Understanding systems of coupled, nonlinear, time-varying ordinary differential equations for analysis and control: non-linearity examples, describing function method, phase plane method, existence and uniqueness of solutions; stability of equilibria and advanced 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; applications.

Program

PhD in Electrical & Control Engineering

Objectives

• Introduce concept of non-lineariy stating examples of non-linearities  Apply describing function method to assess non-linear system stability  Apply phase plane method to analyse non-linear system transient response and stability.  State and assess conditions for local and global existence and uniqueness of solutions of a nonlinear time-varying state equation.  Apply Lyapunov's direct and indirect methods for determing stability of equilibria.  Apply advanced stability analysis techniques, including Lasalle's invariance principle.  Define the input-to-state stability and input-output stability  Determine whether a given system can be linearized through state or output feedback and apply these techniques.  Determine whether a given system can be controlled through backstepping or sliding mode control and apply these techniques  State applictions for non-linear control and get familiar with MATLAB aid