Variational Calculus and Optimal Control Theory

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Lecturer:

Tutor:

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: