Introduction to Systems and Control Theory; Dynamical Systems (4V+2U, 9.0 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)|
|4||V||Lecture||6.0 CP||56 h||124 h|
|2||U||Exercise class (in small groups)||3.0 CP||28 h||62 h|
|(4V+2U)||9.0 CP||84 h||186 h|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. irreg. SuSe|
|Level|| Bachelor (Specialization)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-TEMA] Industrial Mathematics|
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
Basic terms and ideas of Systems and Control Theory as well as their applications will be discussed. In particular, the following contents will be covered:
- representation of time-discrete and continuous linear and non-linear dynamic systems,
- stability of dynamic systems,
- accessibility, controllability, observability,
- feedback rule.
- basics: existence and uniqueness,
- autonomous equations,
- stability theory,
- nonlinear systems, local theory, theorem of Hartman-Grobman, non hyperbolic equilibrium points and Lyapunov theory,
- periodic orbits, Poincaré Bendixon and applications, invariant sets,
- bifurcation theory,
Competencies / intended learning achievements
In the part "Dynamical Systems", they have studied methods for qualitative treatment of dynamic systems and are able to apply them. The focus is on the behavior of solutions of ordinary differential equations under the influence of varying parameters in a system. The techniques taught are very useful for the study of nonlinear partial differential equations and control theory as well as for the study of practical problems that are modeled by using differential equations.
- E. Zerz: Introduction to Systems and Control Theory,
- J.W. Polderman, J. Willems,: Introduction to Mathematical Systems Theory,
- H.W. Knobloch, H. Kwakernaak, Lineare Kontrolltheorie,
- D. Hinrichsen, A.J. Pritchard, Mathematical Systems Theory I,
- E.D. Sontag, Mathematical Control Theory.
- J.K. Hale, H. Kocak: Dynamics and Bifurcations,
- H. Heuser: Gewöhnliche Differentialgleichungen,
- B. Marx, W. Vogt: Dynamische Systeme,
- J.W. Prüss, M. Wilke: Gewöhnliche Differentialgleichungen und dynamische Systeme.
- K. Burg, H. Haf, F. Wille, A. Meister: Höhere Mathematik für Ingenieure. Band III: Gewöhnliche Differentialgleichungen, Distributionen, Integraltransformationen.
Requirements for attendance (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-14-11-M-3] Introduction to Numerical Methods (M, 9.0 LP)