"Classifying systems as linear and nonlinear is like classifying the Universe as bananas and non-bananas" - unknown.
This page: www.ece.gatech.edu/~magnus/ece6552.html
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.
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.
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.
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.
|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)|
|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. 30, 11:30am-2:20pm-||FINAL EXAM