Nonlinear Dynamical Systems and Control

Overview

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ABOUT THE COURSE: The course will provide an introduction to stability and control of nonlinear systems described by ordinary differential equations. The first part of the course will focus on the asymptotic analysis of nonlinear systems through Lyapunov function methods. The second part of the course will provide applications of the Lyapunov function approach to control of linear and nonlinear systems. The specific topics include robust control, adaptive control, and feedback linearization.INTENDED AUDIENCE: PG/PhD studentsPREREQUISITES: B. Tech/B.E with a background in Control Systems or Linear Control SystemsINDUSTRY SUPPORT: Aerospace Industry/Chemical Process Industry

Syllabus

Week 1: Theory:Introduction and preliminaries - Examples and definitions of nonlinear models; state and equilibrium; existence and uniqueness through examples

Week 2:Theory:Existence and uniqueness of solutions, dependence on initial conditions
Week 3:Theory:Stability Theory I - Lagrange, Lyapunov, and asymptotic stability, Lyapunov method and theorems
Week 4:Theory:Stability Theory II - Invariant set theorems and Chetaev’s theorem for instability
Week 5:Theory:Linear Systems and Linearization
Week 6:Theory:Construction of Lyapunov functions
Week 7: Applications:Robust stability and Lure problem - Structured and sector uncertainities

Week 8:Applications:Passivity and dissipativity - General theory, Applications to mechanical and electrical systems
Week 9:Applications:Stable adaptive control - Estimation, indirect, and direct adaptive control
Week 10:Applications:Lyapunov function theory for control problems - General form, specialization to linear systems, linearization, and cascade systems
Week 11:Applications:Optimal control and inverse optimality
Week 12:Applications:Model predictive control