ECE 688 - Nonlinear Systems
Instructor
Professor David Wang
Course description
In this course, we cover classical and modern approaches to the analysis of finite-dimensional, deterministic, nonlinear systems modeled by ordinary differential equations. Tentative topics include: equilibrium points, linearization, phase flows, second order systems, existence and uniqueness of solutions to nonlinear differential equations, Lyapunov stability, the invariance principle, input-to-state stability, input-output stability, feedback linearization, introduction to nonlinear control
Course prerequisites
ECE 682 and undergraduate knowledge of calculus and linear algebra.
Required text
There is no required text for this course. Instructor will write notes on the black board. The optional textbook is Nonlinear Systems, 3rd edition, H.K. Khalil.
Additional references
- Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach, W. M. Haddad, V. Chellaboina.
- Nonlinear Systems Analysis, 2nd edition, M. Vidyasagar.
- Nonlinear Control Systems II, A. Isidori.
- Nonlinear Systems: Analysis, stability and control, S. Sastry.
- ℒ2-Gain and Passivity Techniques in Nonlinear Control, A. van der Schaft.
- Ordinary Differential Equations, V.I. Arnold.
Evaluation
- 50% Final exam
- 30% Assignments. Done in groups. Includes peer assessment marks
- 20% Group course project: presentation, simulation and report.
Tentative topics list
- Introduction to nonlinear systems
- Mathematical preliminaries
- Lyapunov stability
- Input-output stability
- Feedback Linearization
- Nonlinear Control Techniques