The Analytical Control Law Of A Coupled Reaction-diffusion Process

Boundary control to stabilize a system of coupled linear plant and reaction-diffusion process was considered by Zhao and Xie. Backstepping transformation with a kernel function and a vector-valued function was introduced to design the control law.For the situation without heat resource in the reaction-diffusion process, the kernel function and the vector-valued function in the transformation were obtained, and the ex-plicit control law is established. However, for the reaction-diffusion process with heat resource, the analytical solutions of the kernel function and the vector-valued function in the transformation were not obtained. Thus, the analytical control law was not estab-lished.In the present paper, the analytical solutions of the kernel function and the vector-valued function in the transformation are obtained. Therefore, the analytical control law is established.