| Course Unit Code | 638-3026/01 |
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| Number of ECTS Credits Allocated | 6 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| HEG30 | doc. Ing. Milan Heger, CSc. |
| ZIM018 | Ing. Ondřej Zimný, Ph.D. |
| Summary |
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| 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. |
| Learning Outcomes of the Course Unit |
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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.
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| Course Contents |
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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.
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| Recommended or Required Reading |
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| Required Reading: |
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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.
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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.
DUPAČOVÁ, Jitka a Petr LACHOUT. Úvod do optimalizace. Praha: Matfyzpress, 2011. ISBN 978-80-7378-176-7.
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| Recommended Reading: |
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| 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. |
REKTORYS, K. Přehled užité matematiky I. 6. přeprac. vyd. Praha: Prometheus, 1995. ISBN 80-85849-92-5.
REKTORYS, K. Přehled užité matematiky II. 7. vyd. Praha: Prometheus, 2000. ISBN 80-7196-181-7.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials, Experimental work in labs |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 20 | 10 |
| Examination | Examination | 80 | 41 |