Université de Fribourg, Suisse
Faculté des Sciences
Département de mathématiques
Geometric control theory
SP 2016
Patrick Ghanaat MA.3115
MA.4115
Course content

Control theory, developed since the 1950s, is a natural extension of the classical calculus of variations. Its goal is to answer the question whether a “system” governed by differential equations can be moved from one given state to another by adjusting suitable control parameters, and how this can be achieved in an optimal way.

Topics: Introduction and examples, controllability for linear systems, functional analysis and the bang-bang-principle, time optimal control for linear systems, Pontryagin's maximum principle, dynamic programming, Hamilton-Jacobi-Bellman equation, existence of optimal controls, Filippov's theorem

Exam preparation

Contents and sample questions

References

Lawrence C. Evans, An Introduction to Mathematical Optimal Control Theory
Wendell H. Fleming, Raymond W. Rishel, Deterministic and stochastic optimal control
Jack Macki, Aaron Strauss, Introduction to optimal control theory
Andrei Agrachev, Yuri Sachkov, Control theory from the geometric viewpoint
E. B. Lee, L. Markus, Foundations of optimal control theory
L. C. Young, Calculus of variations and optimal control theory