| Course Unit Code | 352-0510/01 |
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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 * | Second Year |
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| Semester when the Course Unit is delivered | Winter 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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| SKU52 | Ing. Jolana Škutová, Ph.D. |
| Summary |
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| Optimality criteria, conditions for optimality, constrains, forms of solution. The analytical and numerical methods of minimization of functions of single and several variables, equality constrains, inequality constrains. Kuhn-Tucker conditions, saddlepoint conditions. Minimizations of functionals, optimal control problems. Bellman’s principle of optimality and dynamic programming. Pontryagin’s minimum principle. Calculus of variations. |
| Learning Outcomes of the Course Unit |
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| The main objective of the subject “Optimization” is acquainting students with methods of static and dynamic optimization. A student must be able to design of the objective function and propose the solution method. In the area of the dynamic optimization a student will be able to design so control, which ensures optimal control from the different point of view, e.g. energy, time, deviation etc. |
| Course Contents |
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Optimality criteria, conditions for optimality, constrains, forms of solution.
The analytical and numerical methods of minimization of functions of single and several variables, equality constrains, inequality constrains, Kuhn-Tucker conditions, saddle point conditions.
Minimization of functionals, optimal control problems.
Bellman’s principle of optimality and dynamic programming.
Pontryagin’s minimum principle.
Calculus of variations.
The method of ag-gregation of state variables in optimal control. |
| Recommended or Required Reading |
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| Required Reading: |
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RAVINDRAN, Auteur, Gintaras V. REKLAITIS and K. M. RAGSDELL. Engineering Optimization. Methods and Applications. New York: John Wilea and Sons, 1983, ISBN 0-471-05579-4.
ROBERTS, Julia a Mykel KOCHENDERFER. Mathematical Optimization [online]. [cit. 2020-04-20]. Dostupné z: https://web.stanford.edu/group/sisl/k12/optimization/
SEWAK, Mohit, Md. Rezaul KARIM a Pradeep PUJARI. Practical Convolutional Neural Networks. Birmingham: Packt Publishing, 2018. ISBN 978-1-78839-230-3. |
KUSYN, Jiří, Antonín VÍTEČEK a Lubomír SMUTNÝ. Teorie řízení: (statická optimalizace). Ostrava: Vysoká škola báňská, 1986.
VÍTEČKOVÁ, Miluše a David JEDLIČKA. Statická optimalizace systémů [online]. 2003 [cit. 2020-04-20]. Dostupné z: http://books.fs.vsb.cz/StatickaOptimalizace/index.htm
VÍTEČKOVÁ, Miluše, Petr PŘIDAL a Tomáš KOUDELA. Systémová analýza: Výukový modul. [online]. Ostrava: VŠB - Technická univerzita Ostrava, 2006 [cit. 2020-04-20]. Dostupné z: http://books.fs.vsb.cz/SystAnal/main.htm
VÍTEČEK, Antonín, Miluše, VÍTEČKOVÁ. Optimální systémy řízení. Ostrava: VŠB - Technická univerzita Ostrava, 1999. ISBN 80-7078-736-8.
RAVINDRAN, Auteur, Gintaras V. REKLAITIS and K. M. RAGSDELL. Engineering Optimization. Methods and Applications. New York: John Wilea and Sons, 1983, ISBN 0-471-05579-4. |
| Recommended Reading: |
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ANDERSON, Brian D. O., John B. MOORE. Optimal Control. Linear Quadratic Methods.
Prentice Hal International, London, 1989, ISBN 0-13-638651-2. |
ŠKUTOVÁ, Jolana. 2004. Neuronové sítě v řízení systémů. Ostrava: VŠB - Technická univerzita Ostrava, 2004.
ANDERSON, Brian D. O., John B. MOORE. Optimal Control. Linear Quadratic Methods.
Prentice Hal International, London, 1989, ISBN 0-13-638651-2.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials, Project work |
| 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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| Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
| Exercises evaluation | Credit | 35 (35) | 0 |
| Project | Project | 15 | 0 |
| Written exam | Written test | 20 | 0 |
| Examination | Examination | 65 (65) | 0 |
| Written examination | Written examination | 45 | 0 |
| Oral | Oral examination | 20 | 0 |