M04 NANTES

Partial differential equations (PDEs) are essential for modeling complex systems, with applications ranging from electrical engineering to fluid mechanics and nuclear fusion. Controlling these infinite-dimensional systems requires advanced tools and methodologies. This course provides a comprehensive overview of stability conditions and control design techniques for PDEs. We will cover all major types of PDEs— parabolic, elliptic, and hyperbolic—with a focus on linear dynamics, including boundary control and boundary output with an abstract viewpoint. Among the different control objectives, design of linear and nonlinear stabilizing output feedback controllers is one of the key problems that will be solved during the classes for various systems. A core objective is solving the challenge of designing constrained stabilizing output feedback controllers, using methodologies such as spectral decomposition, the method of characteristics, and Lyapunov functionals—each chosen based on the equation class. Comparisons with existing classical methods for finite-dimensional systems will be drawn all along the courses. Topics:- Partial differential equations - Transport equations - Reaction diffusion equations - Semigroup theory - Lyapunov functionals - Linear and nonlinear controllers - Output feedback designs