Welcome to the website of ESE-680 Fall 2011
Optimal Control Theory
Time and Location
Mondays and Wednesdays, 1:30-3:00 PM, in Towne 307.
Prof. George J. Pappas, Department of Electrical and Systems Engineering.
Calculus of Variations and Optimal Control Theory: A Concise Introduction, by Daniel Liberzon.
Other books/papers will be provided.
The goal of this special topics course is to read the textbook. Topics will include:
The goals of the course; path optimization vs. point optimization; basic facts from finite-dimensional optimization.
Calculus of variations
Examples of variational problems; Euler-Lagrange equation; Hamiltonial formalism and Legendre transformation; mechanical interpretation; constraints; second variation and Legendre's necessary condition; weak and strong extrema; conjugate points and sufficient conditions.
The maximum principle
Statement of the optimal control problem; variational argument and preview of the maximum principle; statement and proof of the maximum principle; relation to Lie brackets; bang-bang and singular optimal controls.
Dynamic programming; sufficient conditions for optimality; viscosity solutions of the HJB equation.
Optimal control on manifolds, model-predictive control, differential game theory, stochastic control.
ESE 500 Linear Systems is required. ESE 617 Nonlinear systems is suggested but not required. Please skim through the book to determine whether you feel comfortable with the text.
This class will be reading style format where research-oriented students will lead the presentation of each lecture. Depending on the number of students, there may be a class project and/or a take home final exam.