Lecturers:
Piermarco Cannarsa, Università di Roma “Tor Vergata”
Michele Palladino, GSSI
Abstract
This course will mainly concern topics in dynamic optimization of finite dimensional control systems. More specifically, we will cover the basic theory related to the necessary conditions for optimality for non-linear optimal control problems and the dynamic programming principle. Using the dynamic programming principle, we will derive the Hamilton-Jacobi equations and we will present in detail the theory of viscosity solutions. Some of the previous topics will be also discussed in the setting of infinite dimensional control systems.
A more detailed syllabus
1) Definition of Control System and of a Optimal Control Problem;
2) Controllability of Linear Systems;
3) Preliminaries on Nonsmooth analysis
4) The Dynamic Programming Principle;
5) The Hamilton-Jacobi Equations;
6) The Method of Characteristics;
7) The notion of Viscosity Solutions;
8) Properties of Viscosity Solutions;
9) Necessary Conditions: the Pontryagin Maximum Principle;
10) Infinite Dimensional Control Systems;
11) Controllability properties for Infinite Dimensional Control Systems;
12) Hamilton-Jacobi for Infinite Dimensional Control Systems.