638-0801/01 – Theory of Optimal Control (TOR)

Gurantor departmentDepartment of Automation and Computing in IndustryCredits7
Subject guarantordoc. Ing. Milan Heger, CSc.Subject version guarantordoc. Ing. Milan Heger, CSc.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2004/2005Year of cancellation
Intended for the facultiesFMTIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
HEG30 doc. Ing. Milan Heger, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 4+3
Combined Credit and Examination 24+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

Lectures
Tutorials
Experimental work in labs

Summary

Basic terms and relationships of optimal control theory, analytic and numeric methods of one and multidimensional static optimisation and classic theory of extreme control of dynamic systems are discussed. The attention is also paid to optimal control with exploitation of linear programming. The end of lectures is aimed to interpretation of dynamic optimisation axioms.

Compulsory literature:

[1] Bryson, A. and Ho, Y.: Applied Optimal Control. Blaisdell Publishing, Walthman, MA., 1969 [2] Vinter, R. : Optimal Control. Birkhauser, Boston. , 2001

Recommended literature:

[1] Bertsekas, D.: Dynamic Programming and Optimal Control (2nd ed). Athena Scientific, Belmont, MA. 2000

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Introduction to the theory of optimal control, static and dynamic optimization, one-dimensional and multi-dimensional tasks, mathematical apparatus and methods for the solution. 2. Analytical methods of static one-dimensional optimization, derivation of necessary and sufficient conditions, approaches and methods of solution. 3. Numerical differential methods of static one-dimensional optimization-Bolzano method, Newton method, the secants method. 4. Numerical methods of static one-dimensional optimization-direct methods, interpolation methods, uniform comparative methods and its modification. 5. Numerical methods of static one-dimensional optimization-adaptive methods, the golden section method, Fibonaci method and some version of method of the dichotomy. 6. Static multi-dimensional optimization - analytical methods for solving tasks without limits, the method of least squares. 7. Static multi-dimensional optimization - analytical methods for solving tasks with a constraint in the form of equalities and inequalities. 8. Static multi-dimensional numerical methods of optimization, deterministic and stochastic methods. 9. Principles and methods of the extremal control and examples of their practical use in metallurgy. 10. Linear programming, basic concepts, the graphical interpretation and solutions, the creation of models and application to hierarchically higher levels of management in metallurgical industry. 11. Linear programming-solving tasks of linear programming of production, nutritional problem, distribution problem and optimization of cutting plans. 12. Dynamic optimization, basic terms, types of criterion functionals, definition of task and the application for optimal control of large energy aggregates and metallurgical units and optimum control circuits. 13. Calculus of variations, Euler equations, applications in tasks of dynamic optimization. 14. Dynamic programming, Bellman principle, the application in tasks of dynamic optimization. 15. The principle of minimum - Pontrjagin principle, the application in tasks of dynamic optimization.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 20 (20) 0
                Other task type Other task type 20  0
        Examination Examination 80 (80) 0
                Written examination Written examination 30  0
                Oral Oral examination 50  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2013/2014 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P Czech Ostrava 1 Compulsory study plan
2013/2014 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies K Czech Ostrava 1 Compulsory study plan
2012/2013 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P Czech Ostrava 1 Compulsory study plan
2012/2013 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies K Czech Ostrava 1 Compulsory study plan
2011/2012 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P Czech Ostrava 1 Compulsory study plan
2011/2012 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies K Czech Ostrava 1 Compulsory study plan
2010/2011 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P Czech Ostrava 1 Compulsory study plan
2010/2011 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies K Czech Ostrava 1 Compulsory study plan
2009/2010 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P Czech Ostrava 1 Compulsory study plan
2009/2010 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies K Czech Ostrava 1 Compulsory study plan
2008/2009 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies K Czech Ostrava 1 Compulsory study plan
2008/2009 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P Czech Ostrava 1 Compulsory study plan
2007/2008 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies K Czech Ostrava 1 Compulsory study plan
2007/2008 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P Czech Ostrava 1 Compulsory study plan
2004/2005 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies K Czech Ostrava 1 Compulsory study plan
2004/2005 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner