ECE6552 - Spring 2018
Nonlinear Control Systems

Magnus Egerstedt

Phone
Email
Office
(404) 894-3484   
magnus@gatech.edu  
TSRB 436B     

Office hours: Wednesdays 1-3 or by appointment


"Classifying systems as linear and nonlinear is like classifying the Universe as bananas and non-bananas" - unknown.

             



COURSE DESCRIPTION
Nonlinear control deals with the analysis and control of systems that are nonlinear, time-varying, or both. At the heart of the matter is the fact that the nonlinear world is significantly different from the linear world, i.e. it is not just a matter of somehow turning the nonlinear systems into linear ones. In this class, we will investigate how nonlinear systems can be analyzed as well as controlled. In particular, we will discuss various notions of stability and develop a general theory of how to establish stability properties for nonlinear systems. Additionally, nonlinear control methods (including "nonlinearifications" of classic, linear methods) will be developed and applied to a number of example domains, including robotics, avionics, and systems biology.

The course will be divided into five parts, corresponding to the following topics:

     (1) Nonlinear Models (why the nonlinear world is significantly different from the linear world)
     (2) Stability Analysis (from Lyapunov to LaSalle)
     (3) Feedback Control (what can linear systems theory tell us about nonlinear control design?)
     (4) Nonlinear Control (how should one design controllers when linear thinking just isn't enough?)
     (5) Geometric Methods (what can the underlying geometry of the system say about its properties?)

COURSE WEBSITE
This page: www.ece.gatech.edu/~magnus/ece6552.html

WORKLOAD
Your responsibilities in this class will fall into two main categories:
1. The homework sets (five homework - one problem set roughly every third week) = 40%. The credit will be divided between programming assignments and theoretical exercises.
2. The midterm and final exams = 20% + 40% = 60% They will cover all the material presented in the class. They will be closed-book, closed-note, closed-calculator exams.

PROGRAMMING
The objective with the programming assignments is to see how to bridge the gap between what's done in class and how to apply it. (The actual programming involved will be very minor.) The assignments will be Matlab-based.

READING
The course textbook is Hassan K. Khalil, Nonlinear Systems, 3rd Ed., Prentice Hall, 2002 (HK). Additional material pertaining to the geometric methods will be based on Shankar Sastry, Nonlinear Systems: Analysis, Stability, and Control, Springer, 1999 (SS).

TIME AND PLACE
The lectures will be held at 12:00pm-1:15pm Tuesdays and Thursdays in Klaus 1456.

PREREQUISITS Some knowledge of linear algebra, linear control systems, and differential equations will certainly make your life a little easier. ECE6550 (or something equivalent) is the perfect background for this course.

HONOR CODE
Altough you are encouraged to work together to learn the course material, the exams and homeworks are expected to be completed individually. All conduct in this course will be governed by the Georgia Tech honor code.




SCHEDULE

 
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Date Lecture subject Reading/Homework

I. NONLINEAR SYSTEMS
Jan. 9 Introduction to nonlinear systems 1(HK)
Jan. 11 Nonlinear models 1,3(HK)
Jan. 16 Solutions to nonlinear systems 3(HK)
Jan. 18 Linear vs. nonlinear 2,3,8(HK)

II. STABILITY ANALYSIS
Jan. 23 Stability notions 4(HK)
Jan. 25 Lyapunov functions #1 4(HK), HW1 due (nonlinear models)
Jan. 30 Lyapunov functions #2 4(HK)
Feb. 1 The invariance principle #1 4(HK)
Feb. 6 The invariance principle #2 4(HK)
Feb. 8 Converse theorems 4(HK)

III. CONTROL DESIGN
Feb. 13 Feedback control #1 5,12(HK)
Feb. 15 Feedback control #2 12(HK), HW2 due (stability)
Feb. 20 Linearizations 12(HK)
Feb. 22 Review
Feb. 27 MIDTERM
Mar. 1 Zero dynamics 13(HK)
Mar. 6 Feedback linearization #1 13(HK)
Mar. 8 Feedback linearization #2 13(HK), HW3 due (control design)

IV. CONTROL LYAPUNOV FUNCTIONS
Mar. 13 Control Lyapunov functions #1 5(SS)
Mar. 15 Control Lyapunov functions #2 5(SS)
Mar. 20 SPRING BREAK - NO CLASS
Mar. 22 SPRING BREAK - NO CLASS
Mar. 27 CLFs and feedback linearizations
Mar. 29 Control barrier functions HW4 due (CLFs)
Apr. 3 CBFs and the Robotarium

V. GEOMETRIC METHODS
Apr. 5 Controllability concepts 11(SS)
Apr. 10 Drift-free control systems 11(SS)
Apr. 12 Nonholonomic systems #1 11(SS)
Apr. 17 Nonholonomic systems #2 11(SS)
Apr. 19 At the research frontier HW5 due (geometric methods)
Apr. 24 Review
Apr. 30, 11:30am-2:20pmFINAL EXAM