Subjects

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Mathematical Fundamentals of Optimal Control and Games Theory - N413015

Title:	Matematické základy optimálního řízení a teorie her
Guaranteed by:	Department of Mathematics (413)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2013 to 2020
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 [HT]
Capacity:	8 / 8 (unknown)
Min. number of students:	unlimited
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Level:

Guarantor:	Kubíček Milan prof. RNDr. CSc.
Is interchangeable with:	M413009

Examination dates Schedule

Annotation -

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.

Last update: TAJ413 (17.12.2013)

Literature -

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

A: Individually according to the project orientation.

Last update: TAJ413 (05.09.2013)

Teaching methods -

Lectures and exercise classes.

Last update: TAJ413 (01.08.2013)

Syllabus -

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.

Last update: TAJ413 (04.10.2005)

Learning resources -

http://www.vscht.cz/mat/Ang/indexAng.html

Last update: Kubíček Milan (27.08.2013)

Learning outcomes -

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

Last update: Kubíček Milan (01.08.2013)

Registration requirements -

Mathematics I, Mathematics II

Last update: Kubíček Milan (01.08.2013)

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