Boundary Control Of A Class Of Reaction - Diffusion Equations

Boundary control for a class of partial integro-differential systems with space and time dependent coefficients is considered. This system not only consists of reaction, ad-vection, diffusion terms, but also the integral item about space. The Neumann boundary condition comes from the Fourier Law in heat conduction. This system models the phys-ical phenomenons like burning process with a chemical reaction, the integral term means that the system has memory function with spatial variable.According to the partial differential equation(PDE) backstepping method, a Volterra-type integral transformation is established that convert the system into a target system, which is exponentially stable, thought selecting a kernel function. A control law is derived from the boundary condition of the target system that transformation satisfied. There exits a mathematical difficulty to solve the kernel equations analytically. Alter-nately, it is to show the existence of the kernel function. Kernel equation is converted into an integral equation by using the characteristic line of PDE. Based on the method of successive approximation and mathematical induction, the existence of kernel equation is proved in the condition of an assumption. Exponential stability of the closed-loop system is achieved via the transformation and it’s inverse. Simulation equations of the closed-loop and the kernel equation are presented, and the simulation results are shown thought figures.Comparing with existed results, this paper considers a more complex reaction diffu-sion system which extends the existed results to more general situation.