654-3026/01 – Optimal Control of process (OŘP)

Gurantor departmentDepartment of Industrial Systems ManagementCredits6
Subject guarantordoc. Ing. Milan Heger, CSc.Subject version guarantordoc. Ing. Milan Heger, CSc.
Study levelundergraduate or graduateRequirementCompulsory
Study languageCzech
Year of introduction2022/2023Year of cancellation
Intended for the facultiesFMTIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
HEG30 doc. Ing. Milan Heger, CSc.
ZIM018 Ing. Ondřej Zimný, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3
Part-time Credit and Examination 18+0

Subject aims expressed by acquired skills and competences

Student will be able to classify and apply individual methods of optimal control theory in praxis. Student will be able to design a succession for control optimization of individual technological aggregates.

Teaching methods

Experimental work in labs


The basic terms and relations of optimal control theory, analytical and numerical methods of one dimensional and multidimensional static optimization and classical theory of extreme regulation of dynamic systems are discussed. Attention is also paid to the optimal management of larger technological units using linear programming. The lecture is focused on the principles of dynamic optimization and the use of artificial intelligence. The subject provides comprehensive information on the problems of calculating the extremes of functions and functions in solving the optimization tasks of controlling technological aggregates and processes.

Compulsory literature:

GRIVA, I., S. G. NASH a A. SOFER. Linear and nonlinear optimization. 2nd ed. Philadephia: Society for Industrial and Applied Mathematics, 2009. ISBN 978-0-898716-61-0. KIRK, D. E. Optimal control theory: an introduction. Dover ed. Mineola: Dover Publications, 2004. ISBN 0-486-43484-2.

Recommended literature:

ANDERSON, B., B. D. OUTRAM a J. B. MOORE. Optimal control: linear quadratic methods. Dover ed. Mineola: Dover Publications, 2007. ISBN 978-0-486-45766-6.

Way of continuous check of knowledge in the course of semester

Written and oral examination.


Other requirements

elaboration of semester project and passing the test


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

1. Issues of optimal process control. Optimization of static and dynamic systems. Introduction to optimal control theory, static and dynamic optimization, one-dimensional and multidimensional problems, mathematical apparatus and methods of solution. 2. Analytical methods of static one-dimensional optimization, derivation of necessary and sufficient conditions for optimal search, approaches and methods of solution. Practical graphical representation of methods in Excel. 3. Numerical methods of static one-dimensional optimization, their importance and individual approaches. Practical use of differential, direct, interpolation, comparative, adaptive methods. 4. Analytical methods of multidimensional static optimization without limitations and limitations. 5. The smallest square method uses it to approximate functions. Using neural networks to approximate functions. Compare both approaches. 6. Numerical methods of multidimensional static optimization, deterministic and stochastic. Using artificial intelligence in solving multidimensional static optimization tasks. Software implementation of these methods with simulations. 7. Principles and methods of extreme regulation and examples of their practical use in metallurgy and related fields. Software implementation of the extreme controller. 8. Linear programming, basic concepts, graphical interpretations and solutions, modeling and application at hierarchically superior management levels in the metallurgical industry. 9. Linear programming - solution of production programming tasks, nutritional problem, distribution problem and optimization of cutting plans. 10. Practical use of solver in Excel for solving linear and nonlinear problems of multidimensional static optimization. 11. Methods of optimization in solving practical problems in logistics. 12. Dynamic optimization, basic concepts, types of purposeful functions, task definition, methods and applications for optimal control of larger energy aggregates and metallurgical units and optimal setting of control circuits. 13. Use of genetic algorithms and solver in Excel for optimizing the acquisition of mathematical descriptions of dynamic systems from experimentally acquired processes.

Conditions for subject completion

Part-time form (validity from: 2022/2023 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 20  10
        Examination Examination 80  41
Mandatory attendence parzicipation: Prerequisite for completing the course is participation in seminars, maximum three absences.

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2022/2023 (N0413A270002) Quality Management and Control of Industrial Systems (S03) Intelligent Control Systems in Industry P Czech Ostrava 1 Compulsory study plan
2022/2023 (N0413A270002) Quality Management and Control of Industrial Systems (S03) Intelligent Control Systems in Industry K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner