352-0910/05 – Optimization (O)

Gurantor departmentDepartment of Control Systems and InstrumentationCredits10
Subject guarantorprof. Ing. Miluše Vítečková, CSc.Subject version guarantorprof. Ing. Miluše Vítečková, CSc.
Study levelpostgraduateRequirementChoice-compulsory type B
YearSemesterwinter + summer
Study languageEnglish
Year of introduction2014/2015Year of cancellation
Intended for the facultiesFS, HGFIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
VIT40 prof. Ing. Antonín Víteček, CSc.,Dr.h.c.
VIT60 prof. Ing. Miluše Vítečková, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 25+0
Part-time Examination 25+0

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Individual consultations
Project work

Summary

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 aggregation of state variables in optimal control.

Compulsory literature:

LEWIS, F. L., SYRMOS, V. L. Optimal Control. Second Edition. John Wiley & Sons, New York, 1995, ISBN 0-471-03378-2. PINCH, E. R. Optimal Control and the Calculus of Variations. Oxford University Press, Oxford, 1993, ISBN 0-19-853217-2. RARDIN, R. L. Optimization in Operations Research. Second Edition. Pearson Higher Education, Hoboken, 2017, ISBN 978-0-13-438455-9. RAVINDRAN, A., RAGSDELL, K. M., REKLAITIS, G. Engineering Optimization. Methods and Applications. Second Edition. John Wiley & Sons, Hoboken, 2006, ISBN-13 978-0-471-53814-9 http://books.fs.vsb.cz/StatickaOptimalizace/index.htm http://books.fs.vsb.cz/Agregace/index.html

Recommended literature:

ALEXEJEV, V. M., Tichomirov, V. M., FOMIN, S. V. Matematická teorie optimálních procesů. Academia, Praha, 1991, ISBN 80-200-0319-3. BURNS, J. A. Introduction to the Calculus of Variations and Control. CRC Press, Taylor & Francis Group, Boca Raton, 2014, ISBN 978-1-4665-7139-1.

Way of continuous check of knowledge in the course of semester

Kontrola zadaného projektu.

E-learning

Other requirements

Elaboration of the project.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Static optimization. Optimization without constraints, optimization with constraints, numerical solution methods. Optimal control of discrete-time systems. Discrete-time linear quadratic regulator, Bellman’s principle of optimality, dynamic programming in discrete-time optimal control. Optimal control of continuous-time systems. Dynamic programming in continuous-time optimal control. Pontryagin minimum principle, calculus of variations. Aggregation method in optimal control. Standard systems, non-robust and robust control.

Conditions for subject completion

Part-time form (validity from: 2014/2015 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)		Min. number of pointsMax. počet pokusů
Examination Examination   3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (P0714D270002) Control of Machines and Processes K English Ostrava Choice-compulsory type B study plan
2024/2025 (P0714D270002) Control of Machines and Processes P English Ostrava Choice-compulsory type B study plan
2023/2024 (P0714D270002) Control of Machines and Processes P English Ostrava Choice-compulsory type B study plan
2023/2024 (P0714D270002) Control of Machines and Processes K English Ostrava Choice-compulsory type B study plan
2022/2023 (P0714D270002) Control of Machines and Processes P English Ostrava Choice-compulsory type B study plan
2022/2023 (P0714D270002) Control of Machines and Processes K English Ostrava Choice-compulsory type B study plan
2021/2022 (P0714D270002) Control of Machines and Processes P English Ostrava Choice-compulsory type B study plan
2021/2022 (P0714D270002) Control of Machines and Processes K English Ostrava Choice-compulsory type B study plan
2020/2021 (P0714D270002) Control of Machines and Processes K English Ostrava Choice-compulsory type B study plan
2020/2021 (P0714D270002) Control of Machines and Processes P English Ostrava Choice-compulsory type B study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

Předmět neobsahuje žádné hodnocení.