SubjectsSubjects(version: 899)
Course, academic year 2021/2022
Mathematical Fundamentals of Optimal Control and Games Theory - N413015
Title: Matematické základy optimálního řízení a teorie her
Guaranteed by: Department of Mathematics (413)
Actual: from 2021
Semester: winter
Points: winter s.:4
E-Credits: winter s.:4
Examination process: winter s.:
Hours per week, examination: winter s.:2/1 C+Ex [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
For type:  
Guarantor: Kubíček Milan prof. RNDr. CSc.
Is interchangeable with: M413009
Examination dates   Schedule   
Annotation -
Last update: TAJ413 (17.12.2013)
The course is focussed on the ability to formulate of the optimal control of nonlinear dynamical systems. Elements of variational calculus are formulated followed by the Pontryagin maximum principle together with numerical methods of solution of resulting equations. Selected chemical engineering problems are solved.
Aim of the course -
Last update: Kubíček Milan prof. RNDr. CSc. (01.08.2013)

Students will be able to formulate simple problems of optimal control of dynamical models and suggest solution methods.

Literature -
Last update: TAJ413 (05.09.2013)

R: Kubíček M.: Optimalizace inženýrských procesů. SNTL Praha 1986. ISBN 05-098-86

A: Individually according to the project orientation.

Learning resources -
Last update: Kubíček Milan prof. RNDr. CSc. (27.08.2013)

Teaching methods -
Last update: TAJ413 (01.08.2013)

Lectures and exercise classes.

Syllabus -
Last update: TAJ413 (04.10.2005)

1. Elements of variational calculus.

2. Euler equation.

3. Transversality conditions. Direct methods.

4. Maximum principle.

5. Formulation of problem and necessary conditions.

6. Control synthesis.

7. Problem with moving ends and transversality conditions.

8. Chemical engineering formulation.

9. Optimal temperature profile in chemical reactor.

10. Numerical algorithms for optimal control.

11. Gradient method in functional space.

12. Games and decision situation, mathematical models.

13. Games in normal form. Matrix games. Saddle points of games.

14. Games in explicit form. Winning strategy.

Registration requirements -
Last update: Kubíček Milan prof. RNDr. CSc. (01.08.2013)

Mathematics I, Mathematics II

Teaching methods
Activity Credits Hours
Obhajoba individuálního projektu 0,5 14
Účast na přednáškách 1 28
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 0,5 14
Práce na individuálním projektu 0,5 14
Příprava na zkoušku a její absolvování 1 28
Účast na seminářích 0,5 14
4 / 4 112 / 112
Coursework assessment
Form Significance
Regular attendance 20
Defense of an individual project 30
Continuous assessment of study performance and course -credit tests 10
Oral examination 40