Stabilization And Boundary Control Of Coupled Reaction-diffusion Process

Not only in the engineering but also in daily life, it is a common problem to control the temperature stability. Generally, the temperature is modeled by the reaction-diffusion equation. So, to study the stabilization problem of reaction diffusion equations is great practical value.In this paper, we mainly use the Backstepping method on a class of the lin-ear coupled reaction diffusion stability from two aspects problems:one is there is not heat source in the internal linear coupled system. In the study of specific problems, for the coupled linear reaction diffusion system without heat source in-side, using Backstepping method can design the controller. First, introducing a reversible Volterra transformation, to transforme the original system into a target system which is exponentially stable; Then find the inverter transformation which is introduced, and then prove that the closed-loop system is exponentially stable with the transformation introduced and it’s inverse; Finally, through the simulations, it shows the effective of the feedback controller for the reaction diffusion system with-out internal heat source. The other is the system contains internal heat source. From the theory of mathematics, the existence of the output feedback design to the reaction-diffusion system is proved, by using the Backstepping method, the existence and uniqueness of solution of the nuclear equation is obtained. and the existence of the output control for system without internal heat source is derived, meanwhile, the exponentially stable of the closed-loop system is derived.Compared with the existing results, the main work of this paper is to solve the system with heat exchange in boundary in accordance with Fourier’s law. Calcu-lation of nuclear equation is mainly matrix computation and differential equations, which requires the calculation of the application of mathematical techniques; For the proof of the second part, it is difficulty in thinking method to prove, by proving mathematically can also obtain the existence of the output feedback.