Control and Analysis of PDE

The control theory found its applications in various contexts of science and technology: the aerodynamics (parameter identification or optimal design), the economy, the dynamic of populations, and in every domain in which one should take an optimal decision according to a cost criterion. These phenomenon are governed by partial differential equations, as the Schrödinger equation, the wave equation, the heat equation, or networks of flexible strings and beams equations. The control in these systems can be distributed (the internal control in a spatial domain), point or boundary control. The first type of controls leads to bounded control operators. The first axe in this formation will be devoted to the study of the controllability, observability, stabilization, the optimal control and the numerical simulation of this systems. The other type of controls lead to unbounded control. The study of well-posed or regular systems in the sense of Salamon-Prichard or in the sense of Weiss, and also their stability and stabilization will be the aim of the second axe in this formation. A particular accent will be focussed on the use of numerical methods (advantage and difficulties) in the control of some partial differential equations: Which approach will be adopted? Continuous or discret? discretecise and control or the converse? The answer to these interesting questions will be given in this formation.