SylabUZ
Course name | Control Theory 1 |
Course ID | 11.1-WK-MATD-TS1-Ć-S14_pNadGenDEYH1 |
Faculty | Faculty of Mathematics, Computer Science and Econometrics |
Field of study | Mathematics |
Education profile | academic |
Level of studies | Second-cycle studies leading to MS degree |
Beginning semester | winter term 2020/2021 |
Semester | 4 |
ECTS credits to win | 7 |
Course type | optional |
Teaching language | polish |
Author of syllabus |
|
The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
Class | 30 | 2 | - | - | Credit with grade |
Lecture | 30 | 2 | - | - | Exam |
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.
Linear algebra, differential equations.
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.).
Conventional lecture; problem lecture.
Auditorium exercises – solving standard problems enlightening the significance of the theory, exercises on applications, solving problems.
Outcome description | Outcome symbols | Methods of verification | The class form |
Final exam and grade.
1. J. Zabczyk, Zarys matematycznej teorii sterowania, PWN, 1991
2. Z. Wyderka, Teoria sterowania optymalnego, skrypty Uniwersytetu Śląskiego nr 397, Katowice, 1987.
1. S. Rolewicz, Analiza funkcjonalna i teoria sterowania, PWN, 1977.
Modified by dr Alina Szelecka (last modification: 18-09-2020 13:46)