This course investigates how dynamical systems should be controlled in the best possible way!
This page: http://users.ece.gatech.edu/~magnus/ece6553.html
Your responsibilities in this class will fall into two main categories:
1. The homework sets (one problem set roughly every third week) = 50%. The credit will be divided between programming assignments and theoretical exercises.
2. The midterm and final exams = 20% + 30% = 50% 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 is done in class and how to actually apply it. (The actual programming involved will be very minor.) The assignments will be Matlab-based.
The course textbook is Arturo Locatelli, Optimal Control: An Introduction, Birkhauser, 2001 (AL) and it will be complemented by the recommended reading Donald E. Kirk, Optimal Control Theory: An Introduction, Dover Publications, 2004 (DK). An excellent additional source is Daniel Liberzon's upcoming book Calculus of Variations and Optimal Control Theory, available for free at https://netfiles.uiuc.edu/liberzon/www/publications.html.
TIME AND PLACE
The lectures will be held at 9:30-11:00 Tuesdays and Thursdays in Van Leer W200.
PREREQUISITS Some knowledge of linear algebra, linear control systems, and differential equations will certainly make your life a little easier. ECE6550 is the perfect background for this course.
Although you are encouraged to work together to learn the course material, the exams and homework are expected to be completed individually. All conduct in this course will be governed by the Georgia Tech honor code.
|Jan. 11||SNOW DAY|
|Jan. 13||SNOW DAY|
|Jan. 18||Introduction to optimization|
|Jan. 20||Equality constraints|
|Jan. 25||Inequality constraints|
|Jan. 27||Numerical methods||6(DK)|
|CALCULUS OF VARIATIONS|
|Feb. 1||Infinite dimensional optimization||4(DK), HW1 (optimization)|
|Feb. 8||Switch-time optimization|
|THE MAXIMUM PRINCIPLE|
|Feb. 10||The Hamiltonian||5(DK), 6(AL)|
|Feb. 15||Terminal constraints||5(DK), 6(AL), HW2 (calculus of variations)|
|Feb. 22||Terminal manifolds||5(DK), 6(AL)|
|Mar. 3||Free final times||5(DK), 6(AL)|
|Mar. 8||Min-time and bang-bang control||5(DK), 6(AL)|
|Mar. 10||Pontryagin's maximum principle||5(DK), 6(AL), HW3 (Bolza problems)|
|Mar. 15||Control and state constraints||5(DK), 6(AL)|
|Mar. 17||Numerical methods||6(DK)|
|Mar. 22||Spring break - NO CLASS|
|Mar. 24||Spring break - NO CLASS|
|Mar. 29||Dynamic programming||3(DK)|
|Mar. 31||Bellman's equation||3(DK), HW4 (the maximum principle)|
|Apr. 7||The Riccati equation||3(AL)|
|Apr. 12||Infinite horizon control||4(AL)|
|Apr. 14||Hamilton-Jacobi theory||2(AL)|
|Apr. 19||Global conditions||2(AL), HW5 (LQ)|
|Apr. 21||Numerical methods||6(DK)|
|Apr. 26||At the research frontier|
|May 5||FINAL EXAM: 8:00-10:50