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Course, academic year 2022/2023

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Mathematical Modeling and Optimal Control - M413009
Title: Matematické modelování a optimální řízení
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021
Semester: summer
Points: summer s.:4
E-Credits: summer s.:4
Examination process: summer s.:
Hours per week, examination: summer s.:2/1, C+Ex [HT]
Capacity: unlimited / unlimited (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
For type:  
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Kubíček Milan prof. RNDr. CSc.
Isoz Martin Ing. Ph.D.
Interchangeability : N413015
Annotation -
Last update: Isoz Martin Ing. Ph.D. (14.05.2019)
The course is focused on the ability to describe engineering problems via a mathematical model based on a set of partial differential equations (PDEs), on transformation of PDEs into a set of ordinary differential equations (ODEs) and on the ability to formulate an optimal control problem for non-linear dynamical systems. In the first part of the semester, we will focus mostly on numerical solution of the standard transport equation, a PDE describing a general balance law of an arbitrary intensive tensorial quantity. Next, elements of the Pontryagin maximum principle are formulated together with numerical methods of solution of resulting equations. Finally, we show how to apply the obtained knowledge in optimal control to systems described by PDEs.
Aim of the course -
Last update: Isoz Martin Ing. Ph.D. (14.05.2019)

Students will be able to numerically solve models involving mass, heat and momentum transfer, to formulate simple optimal control problems and to design solution methods for the formulated problems.

Literature -
Last update: Isoz Martin Ing. Ph.D. (14.05.2019)

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

A: Individually according to the project orientation.

Learning resources -
Last update: Kubová Petra Ing. (01.05.2019)

Teaching methods -
Last update: Kubová Petra Ing. (01.05.2019)

Lectures and exercise classes.

Syllabus -
Last update: Isoz Martin Ing. Ph.D. (14.05.2019)

1. Mathematical modeling of heat and mass transfer.

2. Mathematical modeling of momentum transfer – Navier-Stokes equations.

3. Models formulated as partial differential equations and their numerical solution.

4. Control of processes involving mass, heat and momentum transfer.

5. Mathematical models with concentrated parameters – systems of ordinary differential equations. Their solution methods.

6. Maximum principle.

7. Formulation of problem and necessary conditions.

8. Control synthesis.

9. Problem with moving ends and transversality conditions.

10. Chemical engineering formulation.

11. Optimal temperature profile in chemical reactor.

12. Numerical algorithms for optimal control.

13. Gradient method in functional space.

14. Methods for optimal control problems for partial differential equations.

Entry requirements -
Last update: Borská Lucie RNDr. Ph.D. (14.05.2019)

Students are expected to have either completed the prerequisite courses Mathematics A and Mathematics B or possess the equivalent knowledge prior to enrolling in the course.

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (14.05.2019)

No requirements.