Fundamentals of Optimal Control Theory
- Unit Coordinator: Jan Cermak
- Programme: Double Degrees
- ECTS Credits: 4
- Semester: 1
- Year: 2
- Campus: Brno University of Technology
- Language: English
- Aims:
The aim of the course is to explain basic ideas and results of the optimal control theory, demonstrate the utilized techniques and apply these results to solving practical variational problems.
- Content:
1. The scheme of variational problems and basic task of optimal control theory.
2. Maximum principle.
3. Time-optimal control of an uniform motion.
4. Time-optimal control of a simple harmonic motion.
5. Basic results on optimal controls.
6. Variational problems with moving boundaries.
7. Optimal control of systems with a variable mass.
8. Optimal control of systems with a variable mass (continuation).
9. Singular control.
10. Energy-optimal control problems.
11. Variational problems with state constraints.
12. Variational problems with state constraints (continuation).
13. Solving of given problems.
- Pre-requisites:
The aim of the course is to explain basic ideas and results of the optimal control theory, demonstrate the utilized techniques and apply these results to solving practical variational problems.
- Reading list:
- Pontrjagin, L. S. - Boltjanskij, V. G. - Gamkrelidze, R. V. - Miščenko, E. F.: Matematičeskaja teorija optimalnych procesov, Moskva, 1961.
- Lee, E. B. - Markus L.: Foundations of optimal control theory, New York, 1967.
- Additional info:
The course familiarises students with basic methods used in the modern control theory. This theory is presented as a remarkable example of the interaction between practical needs and mathematical theories. Also dealt with are the following topics: Optimal control. Pontryagin's maximum principle. Time-optimal control of linear problems. Problems with state constraints. Singular control. Applications.
