Motivation: Virtually all physical systems are non-linear. While many systems can be approximated as linear systems (generally close to the equilibrium point of the system), in many situations this might not be possible, or the analysis may not be restricted to this region. Examples include the pendulum equation, the Hopfield model for neural networks, the Van der Pol equation for oscillations in vacuum tube circuits. The tools required for the analysis and control of such systems are very different from those used for linear systems, and this course provides an introduction to these various tools.
- Mathematical preliminaries- Normed vector spaces, Hilbert spaces, existence and uniqueness of solutions of nonlinear differential equations are covered
- Analyzing the systems- phase-plane method, describing function method
- Notions of stability- limit cycles and Lyapunov stability theory, feedback linearization
- Differential Geometric methods
- Control- concepts are then applied to the control of non-linear systems; feedback linearization
- Parameter sensitivity analysis; numerical tools for nonlinear parameter estimation
- Research case studies- singular perturbations, passivity based approach
Pre-requisites: Any course on linear control would be useful, but is not strictly necessary- the required concepts can be picked up (speak to the course instructor)
Texts: 267011M.Vidyasagar, “Nonlinear systems analysis”, Second Edition, Prentice Hall, 1993.267011H.Khalil, “Nonlinear Systems”, Macmillan Publishing Company, NY, 1992.
Nonlinear control of a pendulum (no small-angle approximation)
Nonlinear Control of A Ground Vehicle Using Lyapunov Techniques
(Written by Rushina Shah)