Markus Schmidmeier

Mathematical Sciences

Florida Atlantic UniversityWelcome 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).

Introduction to Optimal Control

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

OverviewOptimal 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.

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.

TextbookDonald E. Kirk,

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

Format of this seminarThe 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 Tremblay June 4, 6 State variable representation (1.2) Lori Watson June 11 Performance measures (2.1) Kristin Tennant June 13 Selecting a performance measure (2.2) Kalyn Trad June 18 Example: Carrier landing of a jet aircraft (2.3) Daniel Jordan June 20, 25 Introduction to dynamic programming (3.1-4) Alysia Tremblay June 27 Example: An optimal control system (3.5) Daniel Jordan July 2 Linear approximation (3.6) Kristin Tennant July 6 Efficiency of Dynamic Programming (3.9) Kalyn Trad July 9 The Hamilton-Jacobi-Bellman equation (3.11) Lori Watson June 11 Invariant subspaces in optimal control theory (M.S. Presentation) Hasala Karunaratne June 11, 1 p.m.

CreditEach of two talks counts for

30%of the grade, in-class contributions make up the remaining40%.

Contact Me

before and after the seminarOffice hours:

561-297-0275Telephone:

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

markus@math.fau.edu.E-mail:

Last modified:by Markus Schmidmeier