352-0910/01 – Optimization (O)

Gurantor departmentDepartment of Control Systems and InstrumentationCredits10
Subject guarantorprof. Ing. Miluše Vítečková, CSc.Subject version guarantorprof. Ing. Miluše Vítečková, CSc.
Study levelpostgraduate
Study languageCzech
Year of introduction1996/1997Year of cancellation2012/2013
Intended for the facultiesHGF, FSIntended 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 Credit and Examination 25+0
Combined Credit and 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

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.

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

Recommended literature:

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

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

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.

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2012/2013 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes P Czech Ostrava Optional study plan
2010/2011 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes K Czech Ostrava Optional study plan
2009/2010 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes P Czech Ostrava Optional study plan
2009/2010 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes K Czech Ostrava Optional study plan
2008/2009 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes P Czech Ostrava Optional study plan
2008/2009 (P2102) Mineral Raw Materials (3902V010) Automation of Technological Processes K Czech Ostrava Optional study plan
2007/2008 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2005/2006 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2004/2005 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava 1 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner