Optimal Decision and Control

The course is a substitute for:

Optimal Decision and Control (E35ORR)
Optimal Decision and Control (X35ORR)

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

The aim of the subject is to explain problems and give the solution of

optimal control and decision problems. Static and Dynamic Optimization

Problems and its Solution. Linear and Nonlinear Programming. Necessary and

sufficient conditions of optimum, Duality of mathematical programming

problems, Least squares problems, Cholesky and Bierman factorization,

Numerical methods of mathematical programming. Game theory. Optimal control

of deterministic and stochastic systems. Predictive control, Maximum

principle, Principle of optimality and Dynamic programming.

Requirements:

Linear Algebra, Control Theory

Syllabus of lectures:

1. Static and Dynamic Optimization problems, Linear programming (LP)

2. Simplex method, duality in LP

3. Introduction to Theory of Games

4. Least Squares (LS), Cholesky factorization, LDU factorization

5. Updating of Factors, QR decomposition, Singular value decomposition (SVD)

6. Nonlinear programming, convex programming, Karush-Kuhn -Tucker

theorem

7. Nonlinear programming, saddle point, duality.

8. Nonlienar programming I.

9. Nonlienar programming II.

10. Nonlienar programming III.

11. Variational methods I.

12. Variational methods II.

13. Dynamic Programming

14. Maximum Principle

Syllabus of tutorials:

The aim of seminars is to understand optimization methods with help of

Optimization Toolbox in MATLAB. To solve given optimization problem.

1. Optimization problems in praxis

2. Optimization toolbox in Matlab

3. Utilization of optimization toolbox

4. Simplex method of linear programming

5. Theory of games, examples

6. Utilization of least squares

7. Modification of least squares

8. Numerical methods of optimization

9. Constrained optimization

10. Solution of given optimization problem

11. Optimal control of dynamic systems, predictive control

12. Variational methods

13. Dynamic programming

14. Maximum principle

Study Objective:

Study materials:

1. Luenberger, D.G.: Linear and Nonlinear Programming. Addison-Wesley Pub.

Co. 1989

2. Boyd S., Vandenerghe L. : Convex Optimization. http://www.stanford.edu/boyd/

3. Bryson A. E. Yu-Chi-Ho: Applied Optimal Control, Blaisdell Publishing

Co., London, 1969

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Computer Science and Engineering (elective course)