Variational Calculus and Optimal Control Theory

Lecturer:

Leopold Herrmann (gar.)

Tutor:

Leopold Herrmann (gar.)

Supervisor:

Department of Technical Mathematics

Synopsis:

Basic notions and results of the calculus of variations and an introduction to the optimal control theory.

Requirements:

Syllabus of lectures:

1-2. Classical problems of the variational calculus. Functional, differential and variation.

3-4. Extrema of a functional. Necessary and sufficient conditions for the existence of extrema. The Euler equation.

5-6. Other problems of the variational calculus. Variational principles of the mathematical physics.

7-8. Variational methods to the solution of equations (boundary value problems in ordinary and partial differential equations).

9-10. Operators in Hilbert spaces. Existence of a minimum of the functional in the energy space, generalized solutions. The Ritz method. The Galerkin method.

11-12. Admissible controls. The optimal control problem.

13-14. The Pontryagin maximum principle.

Syllabus of tutorials:

1-2. Classical problems of the variational calculus. Functional, differential and variation.

3-4. Extrema of a functional. Necessary and sufficient conditions for the existence of extrema. The Euler equation.

5-6. Other problems of the variational calculus. Variational principles of the mathematical physics.

7-8. Variational methods to the solution of equations (boundary value problems in ordinary and partial differential equations).

9-10. Operators in Hilbert spaces. Existence of a minimum of the functional in the energy space, generalized solutions. The Ritz method. The Galerkin method.

11-12. Admissible controls. The optimal control problem.

13-14. The Pontryagin maximum principle.

Study Objective:

Study materials:

[1] Georg M. Ewing: Calculus of Variations with Applications. (Mathematics Series.) Dover Publ. 1985, ISBN 0-486-64856-7.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon	roomKN:D-104 Herrmann L. 17:45–19:15 (lecture parallel1) Karlovo nám. konzultační místnost KD104
Tue
Fri
Thu
Fri

The course is a part of the following study plans: