EE653

EE 653 – Optimal Control Theory

Spring 2020  Course Information

Instructor: Prof. H. Isil Bozma

Prerequisites : Basic control theory,  matrix algebra, working knowledge of Matlab & Simulink, Some level of C programming.

Class:  Lectures: Mondays 9-11 @  KB Dag Ozay, Wednesdays  11-12 Shannon

Textbooks:  Optimal Control Theory, D. Kirk

Grading: All grades are available.

Grading will be based on in class participation,  projects, two midterms,  and a term project.

Midterm 1 20%,   Midterm 2 30 %, Projects 50%

Grades: Pls follow this link to access all your grades.

Syllabus and Tentative Schedule: Including readings.

 

Week  2 (10-14 Feb)

Chapter 1.1, 1.2 :  Introduction and  review

Review.pdf

Week 3 ( 187- 21 Feb  )

 Chapter 2.1 4.1: Optimal Control Problem,

Fundamental concepts

Calculus of variations

Week 4 ( 24 – 28 Feb )

Chapter 4.2-4.4: Extrema of Functionals,

hw1

Week 5 (2 – 6 March)

Extrema of Functionals (cont.)

Week 6 (9 – 13 March )

Chapter 4.5 Constrained Optima

Constrained extrema

hw2

Week 7 (16 – 20 Mar -> 6 – 10 Apr)

Chapter 6 Numerical Methods

Runge Kutta, Matlab code

Week 8 (23 – 27 Mar  ->  13 – 17  Apr)

Chapter 5.1 Variational Approach to  Optimal Control

Week 9 ( 31 Mar – 3 Apr -> 20  – 24 Apr)

Chapter 5.2 : Linear Regulator s

Week 10 (6 – 10  April -> 27 Apr – 1  May)

Chapter 5.3: Pontryagin’s Minimum Principle

Week 11 (13 – 17 April  -> 4 – 8 May)

Chapter 5.4: Minimum Time Problems

Matlab sims

Week 12 (20 – 24 April -> 11 – 15 May )

Chapter 3.1-3.3  Principle of Optimality

Term project papers — To be finalized.

Week 13 (27 Apr –  1 May -> 18 – 22 May )

 Cha 3.4 – 3.9 Dynamic Programming

Week 14 (4 – 9 May -> 25 – 29 May)

 Chapter 3.11 Hamilton-Jacobi

      Midterm 2

    Term Project

You will be required to do  a course  term project. The project will require the application of  optimal control  methodologies. You will be doing some paper and book search. The proposal will be maximumtwo pages and should include the following

·          Problem Statement

·         Related Literature

·         Problem Formulation including

o        System parameters

o        The state variables

o        The control variables

o        The performance index

o        Constraints

o        Euler-Lagrange Equations

Finding the optimal control

o        Set values for all the parameters

o        Initial values for all the variable

o        You must present simulation results done in a statistical manner

o        You must present a conclusion regarding your work

You will be required to give a 5 minute demo presentation at the end of the semester along with a rar file that contains your fully documented source code and a readme file, the project report and the PPT presentation.

You are expected to do some literature survey (papers, etc. not just web sites!) and relate what you are doing to the work described therein. BE SURE TO REFER TO ANY LITERATURE/EXTERNAL CODE you have examined or used.

A separate REFERENCE section must be added to the end of all your reports.

Again, I assume that the projects have not been or are currently being done for other courses, etc. 1.

Your problem statement must clearly all the following items including their mathematical definitions

Dynamic Optimization Routines

The routines from the book “Dynamic Optimization” by A.E. Bryson.

 Dynopt — Dynamic Optimization Routines