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
Get acquaintance with some basic problematic related to control theoy for ode
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
Traditional lectures
Type of Assessment
Colloquium
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.