SylabUZ
Nazwa przedmiotu | Control Theory 1 |
Kod przedmiotu | 11.1-WK-MATED-CT1-S22 |
Wydział | Wydział Matematyki, Informatyki i Ekonometrii |
Kierunek | Mathematics |
Profil | ogólnoakademicki |
Rodzaj studiów | drugiego stopnia z tyt. magistra |
Semestr rozpoczęcia | semestr zimowy 2023/2024 |
Semestr | 2 |
Liczba punktów ECTS do zdobycia | 7 |
Występuje w specjalnościach | Mathematical modelling |
Typ przedmiotu | obieralny |
Język nauczania | angielski |
Sylabus opracował |
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Forma zajęć | Liczba godzin w semestrze (stacjonarne) | Liczba godzin w tygodniu (stacjonarne) | Liczba godzin w semestrze (niestacjonarne) | Liczba godzin w tygodniu (niestacjonarne) | Forma zaliczenia |
Wykład | 30 | 2 | - | - | Egzamin |
Ćwiczenia | 30 | 2 | - | - | Zaliczenie na ocenę |
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
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.
Opis efektu | Symbole efektów | Metody weryfikacji | Forma zajęć |
Activity of students during classes. Final grade controlling if student pass the minimal level of learning efects.
The final note of Control theory 1 depends on the note of classes (40%) and the note of the exam (60%).
Student is able to pass the exam if he obtained previously the positive note of classes.
1. J. Zabczyk, Mathematical control theory, an Introduction, Birkhauser 1996
2.H. Trentelman, H. Stoorvogel, Control theory for linear systems, Springer 2001
1. S. Rolewicz,Functional Analysis and control theory, linear systems, Mathematics and its applications, Springer 1987
Zmodyfikowane przez dr Ewa Sylwestrzak-Maślanka (ostatnia modyfikacja: 10-04-2024 15:55)