Optimal Decision and Control

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:

Syllabus of lectures:

1. Optimal Control and Decission, Static and Dynamic Problems

2. Linear Programming,

3. Simplex method

4. Introduction to Theory of Games

5. Mathematical Programming, Saddle Point, Duality

6. Quadratic Forms Minimization

7. Cholesky Factorization, LDU Factorization, Updating of Factors

8. Numerical Methods of Mathematical Programming

9. Constrained optimization methods

10. Optimal control of dynamic systems, predictive control

11. Variational methods

12. Principle of Optimality and Dynamic Programming

13. Maximum Principle

14. Numerical Methods in Dynamic Optimization

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. 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:

• Cybernetics and Measurements - Control Engineering- structured studies (compulsory course)