AOE5244: Optimization Techniques, Fall 2017

Cource Description

This course will cover analysis and design techniques in optimal control systems and differential games. Topics will include optimization under constraints, KKT conditions, multiplier methods, descent methods, quasi-Newton methods, calculus of variations, Pontryagin's maximum principle, matrix Riccati equations and application to aircraft autopilot design, nonlinear optimality and relation to Hamilton's principle in physics, suboptimal control, dynamic programming, duality of optimal control and optimal estimation, differential games, Hamilton-Jacobi-Isaacs equation, H∞ control, value and policy iteration, approximation methods with reinforcement learning to adapt to optimal control solutions without knowing the full system dynamics. Tentative Syllabus: Here

Instructor

Prof. Kyriakos G. Vamvoudakis
Room 226, Randolph Hall,
Kevin T. Crofton Dept. of Aerospace and Ocean Eng.,
Virginia Tech, Blacksburg,
VA 24061-0203 USA
E-mail: kyriakos at gatech.edu
Website: http://kyriakos.ae.gatech.edu/
Telephone: +1 (540)-231-6707

Office Hours

TuThu, 11:00am - 12:30pm, Randolph Hall 226

Please email or phone me in advance to schedule for an appointment. If you have any questions about the course, please send me email. I will try to respond as quickly as possible. Additionally, I will share questions that are particularly good (and their answers) with the rest of the class by broadcasting my answer to the entire class. If you plan to come to office hours for questions about homework, please be prepared to show attempts at solving the problem that you prepared before coming.

Lecture Time and Place

TuTh, 3:30pm - 4:45pm, New Classroom Building 270

Course Credit

Units: 3

Prerequisites

Competency in linear algebra, nonlinear dynamical systems and linear control systems.

Textbooks

The course will follow closely:

• F. L. Lewis, D. Vrabie, V. L. Syrmos, Optimal Control, John Wiley and Sons, 2012 (ISBN: 978-0-470-63349-6). Details available here.

• D. Liberzon, Calculus of Variations and Optimal Control Theory: A Consise Introduction, Princeton University Press, 2012 (ISBN: 978-0-691-15187-8). Details available here.

• T. Basar, G. J. Olsder, Dynamic Noncooperative Game Theory, Vol. 23, SIAM, 1999 (ISBN: 978-0-89871-429-6). Details available here.

• D. Vrabie, K. G. Vamvoudakis, F. L. Lewis Optimal Adaptive Control and Differential Games by Reinforcement Learning Principles, Control Engineering Series, IET Press, 2012 (ISBN: 978-1-84919-489-1). Details available here.

Website

The website for this course will be maintained on Canvas and here.