Boundary Control Of Reaction-diffusion Process In Ball

It is one of the hot topics in the field of control theory that the boundary control problems of PDE in the past few years. Due to the multidisciplinary pervasion in the theory and methods, boundary control, which is a form of distributed param-eter control, is a hot topic in present with wide application prospect. This paper focuses on boundary control problems of reaction-diffusion equation in spherical re-gion. Based on the structure of the equations, state feedback controller and output feedback controller on observer are designed in this paper by the method of Back-stepping with integrator. First, the original system is transformed to one dimension reaction-diffusion equation by the method of spherical coordinate transformation and the assumption of central symmetric. Then, the original system is transformed to target system, by the method of invertible coordinate transform with a kernel, on suitable boundary conditions. This transformed system can be proved to be exponential stability by Lyapunove analysis. It is can be proved that the kernel of the transformation is the solution of Klein-Gordon hyperbolic PDEs, then these hyperbolic PDEs are transformed to equivalent integral equations. And it also can be proved that the kernel equation has a unique solution by the method of succes-sive approximations, which generates state feedback controller and output feedback controller in closed-loop system. At last, exponential stability of the original system can be proved by the invertible of the transformation.