“Mathematical Methods For Control Theory (part III)” by Jérôme Lohéac, Umberto Biccari & Víctor Hernández-Santamaría

The aim of this course is to present a systematic overview of several mathematical tools which are commonly employed in control theory. The lectures will be organized in various thematic modules, each one developed around a different type of model. We will treat both theoretical and numerical aspects.
The lectures during February will be devoted to the controllability of the heat equation and Carleman inequalities.

Two sessions will be delivered by Jerome Loheac from University of Lorraine (CRAN), Nancy, France and will be entitled:

Pontryagin maximum principle, consequences and extentions
In these talks, I will introduce the Pontryagin maximum principle. This principle gives necessary conditions on optimal control problems. I will give different examples illustrating how this principle can help for finding optimal controls. I will in particular focus on time optimal control problems and will give some extensions of this principle to some infinite dimensional control problem.