Variational Calculus and Optimal Control Theory
Code  Completion  Credits  Range 

W01T004  ZK  30 
 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:

12. Classical problems of the variational calculus. Functional, differential and variation.
34. Extrema of a functional. Necessary and sufficient conditions for the existence of extrema. The Euler equation.
56. Other problems of the variational calculus. Variational principles of the mathematical physics.
78. Variational methods to the solution of equations (boundary value problems in ordinary and partial differential equations).
910. Operators in Hilbert spaces. Existence of a minimum of the functional in the energy space, generalized solutions. The Ritz method. The Galerkin method.
1112. Admissible controls. The optimal control problem.
1314. The Pontryagin maximum principle.
 Syllabus of tutorials:

12. Classical problems of the variational calculus. Functional, differential and variation.
34. Extrema of a functional. Necessary and sufficient conditions for the existence of extrema. The Euler equation.
56. Other problems of the variational calculus. Variational principles of the mathematical physics.
78. Variational methods to the solution of equations (boundary value problems in ordinary and partial differential equations).
910. Operators in Hilbert spaces. Existence of a minimum of the functional in the energy space, generalized solutions. The Ritz method. The Galerkin method.
1112. Admissible controls. The optimal control problem.
1314. The Pontryagin maximum principle.
 Study Objective:
 Study materials:

[1] Georg M. Ewing: Calculus of Variations with Applications. (Mathematics Series.) Dover Publ. 1985, ISBN 0486648567.
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: