Mathematical Methods Of Optimal Control (FSI-9MOR)

Academic year 2020/2021
Supervisor: prof. RNDr. Jan Čermák, CSc.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech or English
Aims of the course unit:
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.
Learning outcomes and competences:
Students will acquire knowledge of basic methods of solving optimal control problems. They will be made familiar with the construction of mathematical models of given problems, as well as with usual methods applied for solving.
Prerequisites:
Differential and integral calculus, ordinary differential equations.
Course contents:
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. Bellman's principle of optimality. Pontryagin's maximum principle. Time-optimal control of linear problems. Problems with state constraints. Applications.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes:
Course-unit credit is awarded on the following conditions: Active participation in seminars. The examination tests the knowledge of definitions and theorems (especially the ability of their application to the given problems) and practical skills in solving of examples. The exam is written (possibly followed by an oral part).
Grading scheme is as follows: excellent (90-100 points), very good
(80-89 points), good (70-79 points), satisfactory (60-69 points), sufficient (50-59 points), failed (0-49 points). The grading in points may be modified provided that the above given ratios remain unchanged.
Controlled participation in lessons:
Attendance at lectures is recommended. Lessons are planned according to the week schedules. Absence from seminars may be compensated for by the agreement with the teacher.
Type of course unit:
    Lecture  10 × 2 hrs. optionally                  
Course curriculum:
    Lecture 1. The scheme of variational problems and basic task of optimal control theory.
2. Dynamic programming. Bellman's principle of optimality.
3. Maximum principle.
4. Time-optimal control of an uniform motion.
5. Time-optimal control of a simple harmonic motion.
6. Basic properties of optimal controls.
7. Optimal control of systems with a variable mass.
8. Variational problems of flight dynamics.
9. Energy-optimal control problems.
10. Variational problems with state constraints.
Literature - fundamental:
1. Pontrjagin, L. S. - Boltjanskij, V. G. - Gamkrelidze, R. V. - Miščenko, E. F.: Matematičeskaja teorija optimalnych procesov, Moskva, 1961.
2. Lee, E. B. - Markus L.: Foundations of optimal control theory, New York, 1967.
3. Alexejev, V. M. - Tichomirov, V. M. - Fomin, S. V.: Matematická teorie optimálních procesů, Praha, 1991.
Literature - recommended:
1. Brunovský, P.: Matematická teória optimálneho riadenia, Bratislava, 1980.
2. Víteček, A., Vítečková, M.: Optimální systémy řízení, Ostrava, 1999.
3. Čermák, J.: Matematické základy optimálního řízení, Brno, 1998.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
D4P-P full-time study D-APM Applied Mathematics -- DrEx 0 Recommended course 3 1 S
D-KPI-P full-time study --- no specialisation -- DrEx 0 Recommended course 3 1 S
D-APM-K combined study --- -- DrEx 0 Recommended course 3 1 S