Markus Schmidmeier
Mathematical Sciences
Florida Atlantic University

Introduction to Optimal Control

Welcome to the Optimal Control Seminar! We meet Monday and Wednesday 11:30 a.m. - 1 p.m. in SE 215, starting June 4, 2012. The course can be taken as a Directed Independent Study (MAT 4906-12, CRN 57254).

Prerequisites

Familiarity with linear algebra and with differential equations. More important: Eagerness to learn about exciting applications of mathematics.

Overview

Optimal control theory --- which is playing an important role in the design of modern systems --- has as its objective the maximization of the return from, or the minimization of the cost of, the operation of physical, social and economic processes.

optimal control is everywhere

In Part I of this course we discuss the use of state variables to capture the mathematical aspects of real life systems and to define performance measures. The topic of Part II is Dynamic Programming as it is used to compute control functions which maximize the performance measures.

Textbook

Donald E. Kirk, Optimal Control Theory, an Introduction, Dover, ISBN-13: 978-0-486-43484-1

Format of this seminar

The seminar consists of student presentations an in-class discussions. The talks --- which are distributed among the participants --- cover sections in the textbook and include a discussion of one of the problems in the book.

Topic
 

Speaker
 

date
 

Problem formulation (1.1) Alysia TremblayJune 4, 6
State variable representation (1.2) Lori WatsonJune 11
Performance measures (2.1) Kristin TennantJune 13
Selecting a performance measure (2.2) Kalyn TradJune 18
Example: Carrier landing of a jet aircraft (2.3) Daniel JordanJune 20, 25
Introduction to dynamic programming (3.1-4) Alysia TremblayJune 27
Example: An optimal control system (3.5) Daniel JordanJuly 2
Linear approximation (3.6) Kristin TennantJuly 6
Efficiency of Dynamic Programming (3.9) Kalyn TradJuly 9
The Hamilton-Jacobi-Bellman equation (3.11) Lori WatsonJune 11
Invariant subspaces in optimal control theory (M.S. Presentation) Hasala KarunaratneJune 11, 1 p.m.

Credit

Each of two talks counts for 30% of the grade, in-class contributions make up the remaining 40%.

Contact Me

Office hours:   before and after the seminar

Telephone:  561-297-0275

Home Page:   http://math.fau.edu/markus

E-mail:   markus@math.fau.edu.


Last modified:  by Markus Schmidmeier