Control of Coupled Systems of Hyperbolic PDEs and applications to Robust Control
Fatiha Alabau Boussouira
Université de Lorraine
Institut Elie Cartan
Abstract: Many complex control problems arise in applications in mechanics, physics, Biology and medicine. These problems are modeled by various types of coupled systems such as Timoshenko beams, string or beams networks in mechanics, reaction-diffusion systems in biology, fuid-structure interactions in naval applications. For realistic control applications, the number of controls may have to be reduced, i.e. the number of controls has to be strictly less that the number of state variables. Such control arise for instance when it is to expensive or not realistic to control all the state variables. The first part of the course present several motivations for the control of coupled system. The second part of the course explains the basic notion for the control for the scalar abstract wave equation, admissibility, and observability properties of the dual problem. It will also introduce the Hilbert uniqueness method (HUM) to solve the control problem. The third part of the course focuses on some recent results for the control of coupled abstract systems and applications to the control of coupled wave systems.