Boundary Control Of Reaction Diffusion Equations

In this paper, we study the boundary control problem of reaction diffusion equations. The reaction diffusion equations include the reaction, convection and diffusion terms, and these reaction diffusion equations are coupled with each other. Because of the complexity of these coupled reaction diffusion equations, in this paper, the method of matrix representation is used to make the original system more easily expressed. The system can be said that the chemical reaction, biological fermentation and other issues in industrial production, the research of the system has a certain value.Dealing with the boundary control problem of the coupled reaction diffusion equations, in this paper, the matrix form Backstepping transformation is used to obtain the kernels equations according to the corresponding conditions, and then the knowledge of the matrix is used to prove the presence of kernels equation group of a display solutions, and then the boundary conditions obtained reaction diffusion equations of control law. By means of inverse transformation that kernels equa-tion is reversible, the Lyapunov function prove the system under the control of the boundary is exponential stability. In order to prove the correctness of the theory, the data simulation of the system is carried out.Compared with the existing results, this paper refers to the matrix tool to solve the boundary control problem of reaction diffusion equations, At the same time, the scope of the reaction diffusion equation group is also generalized, In the original study diffusion matrix is only the n order unit matrix. In this paper, we extend the scope of the matrix, but also to promote the reaction diffusion equations, so that this paper has some research value.