Course detail
Fundamentals of Optimal Control Theory
FSI-SOR-AAcad. year: 2024/2025
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.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Examination: 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 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.
Attendance at lectures is recommended, attendance at seminars is obligatory and checked. Lessons are planned according to the week schedules. Absence from seminars may be compensated for by the agreement with the teacher.
Aims
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.
Study aids
Prerequisites and corequisites
Basic literature
Howlett, P.G. - Pudney,P.J.: Energy-Efficient Train Control,Springer, London, 1995.. (EN)
Recommended reading
Lee, E. B. - Markus L.: Foundations of optimal control theory, New York, 1967. (EN)
Pontrjagin, L. S. - Boltjanskij, V. G. - Gamkrelidze, R. V. - Miščenko, E. F.: Matematičeskaja teorija optimalnych procesov, Moskva, 1961. (EN)
Classification of course in study plans
- Programme N-MAI-P Master's 1 year of study, summer semester, compulsory
- Programme N-AIM-A Master's 2 year of study, summer semester, compulsory
- Programme N-MAI-A Master's 1 year of study, summer semester, compulsory
- Programme C-AKR-P Lifelong learning
specialization CLS , 1 year of study, summer semester, elective
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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.
Exercise
Teacher / Lecturer
Syllabus
2. The basic task of optimal control theory demonstrated by examples.
3. Time-optimal control of an uniform motion demonstrated by examples.
4. Time-optimal control of a simple harmonic motion demonstrated by examples.
5. Linear time-optimal control problems with fixed boundaries.
6. Linear time-optimal control problems with moving boundaries.
7. Optimal control of systems with a variable mass demonstrated by examples.
8. Optimal control of systems with a variable mass demonstrated by examples (continuation).
9. Optimal control of systems with a variable mass demonstrated by examples (continuation).
10. Problem of an energy optimal control of a train.
11. Nonlinear programming problems in optimal control problems.
12. Variational problems with state constraints.
13. Variational problems with state constraints (continuation).