1. Alberto Bressan and Benedetto Piccoli
Introduction to the Mathematical Theory of Control - AIMS on Applied Math. Vol. 2 , 2005. 2. A.Agrachev, Yu.Sachkov, Control Theory from the Geometric Viewpoint, Springer Verlag, 2004 3. Gamkrelidze R.V. Principles of Optimal Control, Plenum Press, 1978.
Learning Objectives
The lecture Course has a goal to provide students with
KNOWLEDGE about fundamental problem settings of mathematical control theory. Addressing essentialy the problems of controllability, optimal control and stability the course starts with an introduction to the supplementary topics of ODE and then proceeds with different methods of analysis of control systems.
EXPERTISE necessary for construction and analysis of models
of mathematical control theory.
Prerequisites
Functional Analysis. Normed spaces and continuous linear maps. Hahn-Banach theorem. Banach spaces. Hilbert spaces. Differential calculus in R^n. Theory of Lebesgue measure. L^p spaces. Holder spaces.
Teaching Methods
Lectures: presentation of the theory contained in the program of the course, with direct interaction between student and teacher, to ensure comprehension of the contents.
Oral examination in the form of a semanar where the students present a topic, which develops the questions treated during the lectures. The examination verifies the comprehension of the material taught, as well as capacity of autonomous reasoning.
Course program
Ordinary differential equations, Linear systems. Non linear systems and linearization.
Control systems. Reachable set. Linear systems. STLC. Lie brackets and controllability.
Optimal control problems: Mayer problem, Bolza problem. Existence of optimal controls. Pontryagin maximum principle. The bang-bang controls. LQ problems.
Existence of optimal controls.
Stability: introduction to Lyapunov theory. Stabilization of linear and nonlinear systems.