Course Name:	Nonlinear Control
Course No.	EE - 43071
Professor:	Dr. Hamid D. Taghirad
Semester:	Fall 83
Room and Time:	Mon and Wed: 8:00-10:00 Room 204
Office Hours:	Mon:    15:00:17:00

This course aims to introduce the analysis of nonlinear system, and the common nonlinear control schemes. The course is divided into two parts, namely analysis and synthesis. In the analysis part, the state space description of nonlinear system is introduced, and the phase portrait analysis of the second order system is elaborated. Stability analysis of the nonlinear system, based on linearization method, and direct method of Lyapunov is explained next, while the stability analysis is completed with Lasalle theorem, absolute stability notion, Popov, and circle criteria, and the stability analysis of time varying nonlinear systems. finally, the analysis of limit cycles is thoroughly elaborated using describing functions. In the synthesis part, after introducing of Lie Alegebra, and required mathematics, Feedback linearization methods for input-state, and input-output cases are described, and backstepping method and sliding mode control is introduced next. To evaluate the expertise of the student in nonlinear control analysis and synthesis,  a thorough and comprehensive design task is performed by them as a term project using Matlab simulations.

The tentative course contents are as following:

Time:	Teaching Contents
Week 1	Introduction: Common nonlinear systems, state space representation, equilibrium point, common behaviors of nonlinear systems, and limit cycles.
Week 2	Phase plane Analysis: 2nd order nonlinear systems, phase portrait graphical representation, singular points.
Week 3	Phase plane Analysis: Graphical and  numerical methods of phase portrait generation, stability analysis of linear systems via phase portrait, stability analysis of nonlinear system with phase portraits.
Week 4	Stability Analysis: Different definition of stability for nonlinear systems, Lyapunov linearization method, Lyapunov direct method, globally asymptotically stability analysis.
Week 5	Stability Analysis: Lyapunov direct method extensions, Lasalle's theorem, time varying nonlinear systems stability theorems, instability theorems
Week 6	Stability Analysis: Absolute stability theorems, Sector nonlinearity, Popov and circle criteria, Lyapunov based controller synthesis.
Week 7	Describing Functions: Limit cycle definition and characteristics, existance theorems, describing function definitions.
Week 8	Describing Functions: Describing function for saturation, relay, dead zone and hysteresis, limit cycle analysis by describing function, limit cycle stability analysis.
Week 9	Midterm Exam
Week 10	Feedback Linearization: Background mathematics, Lie algebra, input-state feedback linearization, feedback linearizability, involutivity, and controllability conditions.
Week 11	Feedback Linearization: input-state feedback linearization algorithm, normal forms, diffeomorphism, comprehensive examples.
Week 12	Feedback Linearization: input-output feedback linearization algorithm, internal dynsmics, zero dynamics, asymptotically minimum phase nonlinear systems, comprehensive example.
Week 13	Back Stepping: Controller general description, required conditions, Back stepping method, controller characteristics, comprehensive example.
Week 14	Sliding mode: General description, sliding surfaces, switching mode controller law, sliding mode controller structure, comprehensive example.
Week 15	Sliding mode: Chattering problem, boundary layer description, sliding condition extension, fixed threshold boundary layer, variable boundary layer, comprehensive example.

 

●	UK Nonlinear Dynamics Groups
●	CalTech Control And Dynamical Systems Group
●	CalTech control engineering virtual library
●	Cambridge U. Control Group
●	Nonlinear E-course in Lund University
●	The Joy of Feedback (1991 Bode Prize Lecture by P. Kokotovic)