Variational Calculus and Optimal Control Theory
Code | Completion | Credits | Range |
---|---|---|---|
W01T004 | ZK | 30B |
- Garant předmětu:
- 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: