638-0801/01 – Theory of Optimal Control (TOR)
| Gurantor department | Department of Automation and Computing in Industry | Credits | 7 |
| Subject guarantor | doc. Ing. Milan Heger, CSc. | Subject version guarantor | doc. Ing. Milan Heger, CSc. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2004/2005 | Year of cancellation | 2020/2021 |
| Intended for the faculties | FMT | Intended for study types | Follow-up Master |
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
Other requirements
Elaboration of semester project
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction