Courses Detail Information

ECE6607J – Nonlinear Systems and Control


Instructors:

Jun Zhang

Credits: 3 credits

Pre-requisites: Graduate Standing

Description:

Graduate course in nonlinear systems and control.

Introduction to nonlinear phenomena: multiple equilibria, limit cycles, bifurcations, complex dynamical behavior. Planar dynamical systems, analysis using phase plane techniques. Input-output analysis and stability. Lyapunov stability theory. Circle and Popov criterion. Feedback linearization, sliding mode control.

• Introduction to Nonlinear Phenomena: Complexity in nonlinear dynamics, Classical examples, Multiple Equilibria, Limit Cycles, Complex Dynamics, Bifurcations

• Second-Order Nonlinear Systems: Phase Plane Techniques, Limit Cycles Poincare-Bendixson Theory, Index Theory

• Input-output analysis and stability: Small Gain Theorem, Passivity, Describing Functions

• Lyapunov Stability Theory: Basic stability and instability theorems, LaSalles theorem, Indirect method of Lyapunov

• Nonlinear Control: Linearization by State Feedback for SISO and MIMO systems,Involutivity, Lie Brackets, FrobeniusTheorem, Zero Dynamics, Inversion, Tracking, Stabilization

Course Topics:

Introduction to Nonlinear Phenomena:Complexity innonlinear dynamics
Classical examples
Multiple Equilibria
Limit Cycles
Complex Dynamics
Bifurcations
Second-Order Nonlinear Systems: Phase Plane
Techniques
Limit Cycles Poincare-Bendixson Theory
Index Theory
Input-output analysis and stability:Small GainTheorem
Passivity
Describing Functions
Lyapunov Stability Theory:Basic stability andinstability theorems
LaSalle’s theorem
Indirect method of Lyapunov
Nonlinear Control:Linearization by State Feedback
for SISO and MIMO systems
Involutivity, Lie Brackets
Frobenius’Theorem, Zero Dynamics
Inversion, Tracking,Stabilization