After the course of “control theory 2” students should be able to solve themselves practical and theoretical problems on the topic of dynamical nonlinear systems and theory of set valued functions.
Wymagania wstępne
Theory of measure and Lebesgue's integral, Control theory 1
Zakres tematyczny
Lecture:
Problems of the theory of optimal control (6 hours).
Controllability and properties of admissible sets of dynamical controlled systems (4 hours).
Support functions and integral maximum rule (2 hours).
Hausdorff metric, continuity of operators (4 hours).
Problem of optimal control as a differential inclusion (2 hours).
Continuity and measurability of multifunctions (4 hours).
Selection problems: minimal, Tschebyshev, barycentric and Steiner point (4 hours).
Selections theorems of Michael and Kuratowski Ryll-Nardzewski (4 hours).
Kakutani fixed point theorem (2 hours).
Filipoff theorem (2 godz.).
Aumann integral and its properties (4 hours).
Connections of control problems with theory of differential inclusions and theorems of the existence of solutions of differtential inclusions (3 hours).
Viability problem (4 hours).
Classes:
Practical problems leading to optimal control problems (2 hours).
Properties of admissible sets in dynamical control systems (2hours).
calculation of support functions and applications of integral maximum rule (1 hour).
Calculation of Hausdorff metric in given spaces (2hours).
Calculation of upper and lower semicontinuity and measurability of given multifunctions (2 hours).
Viability problem and properties of tangent cones (2 hours).
Test (2 hours)
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
Activity of students during classes. Final grade controlling if student pass the minimal level of learning efects.
The final note of Control theory 2 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.
Literatura podstawowa
M. Kisielewicz, Differential Inclusions and Optimal Control, PWN – Kluwer Acad. Publ. 1991,
J. P. Aubin, A. Cellina, Differential Inclusions, Springer Verlag 1984,
S. Rolewicz,Functional Analysis and control theory, linear systems, Mathematics and its applications, Springer 1987
Literatura uzupełniająca
1. J. Zabczyk, Mathematical control theory, an Introduction, Birkhauser 1996
Uwagi
Zmodyfikowane przez dr Ewa Sylwestrzak-Maślanka (ostatnia modyfikacja: 10-04-2024 16:07)
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