1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. WMIiE - oferta ERASMUS - Program Erasmus
5. Control Theory 1

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Control Theory 1 - opis przedmiotu

Cel przedmiotu

After the course of “Control theory 1” students should be able to solve themselves practical and theoretical problems on the topic of dynamical linear systems.

Wymagania wstępne

Zapisz zmiany

Linear algebra, differential equations.

Zakres tematyczny

Lecture:
1. Dynamical systems – definitions and classification (4 h.).
2. Main theorem on the smooth system (2 h.).
3. Costs functional - problems of Meyer, Lagrange and i Bolza (2 h.).
4. Differential types of controllability (2 h.).
5. Linear dynamical systems, fundamental matrix (2 h.).
6. Gram matrix, its properties and connections with global controllability (2 h.).
7. Theorems of Kalman’s type for discrete and continuous linear dynamical systems (4 h.).
8. Linear-quadratic problem (2 h.).
9. Properties of attainable set, emission zone and the set of attainable controls (2 h.).
10. Theorems on properties of the attainable set: convexity, boundedness, compactness (4 h.).
11. Extremal controls (2 h.).
12. Integral maximum rule (2 h.).

Class
1. Linear equations and their fundamental matrix different methods of solving (4h.).
2. Linear dynamical systems and „0-1” fundamental matrix (2 godz.).
3. Gram matrix solving and its connections with global controllability (2 h.).
4. Solving of global controllability of discrete and continuous linear dynamical systems by Kalman’s methods (6 h.).
5. Solving of linear-quadratic problem (4 h.).

6. Properties of attainable set, emission zone and the set of attainable controls (2 h.).
7. Examples of the nonexistence of optimal controls without convexity or compactness of attainable controls (2 h.).
8. Extremal controls for linear dynamical systems (4 h.).
9. Applicability of the integral maximum rule (2 h.).

Metody kształcenia

Conventional lecture; problem lecture.
Auditorium exercises – solving standard problems enlightening the significance of the theory, exercises on applications, solving problems.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Final exam and grade.

Literatura podstawowa

1. J. Zabczyk, Zarys matematycznej teorii sterowania, PWN, 1991
2. Z. Wyderka, Teoria sterowania optymalnego, skrypty Uniwersytetu Śląskiego nr 397, Katowice, 1987.
3. E.D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, 2nd ed., Springer-Verlag New York, 1998

Literatura uzupełniająca

1. S. Rolewicz, Analiza funkcjonalna i teoria sterowania, PWN, 1977.

Uwagi

Zmodyfikowane przez dr Joachim Syga (ostatnia modyfikacja: 28-04-2022 15:42)