Stabilization And Boundary Control Of Cascaded Reaction-diffusion Process

Stability of temperature is a requirement in the engineering problem such as chem-ical reaction or biological fermentation. Generally, the temperature is modeled by the reaction-diffusion equation. For the rich physical backgrounds, many reaction-diffusion equation were researched widely.In this paper, we focus on boundary control problem of a PDE-ODE system cascad-ed at intermediate point with Neumann interconnections. In the study of specific prob-lem, the system cascaded at intermediate point with Neumann interconnections, using Backstepping method can design the controller, a revised backstepping transformation is introduced. The inverse transformation is also obtained. Stabilization of the closed loop is approved.In this paper, based on the Volterra transformation a new backstepping transforma-tion is introduced. The new transformation contains both Volterra integrals and Fredholm integrals, in which there are four kernels. Since the number of kernels is increased the kernel equations and computation are more complicated, especially, it is a challenge to solve the kernel equations. Fortunately, through a series of mathematical tricks, the exact solutions of kernels are obtained. A control law is obtained specifically via these kernel-s. To establish the stability of the closed loop, the inverse transformation is derived by the same procedure, and the stability of the closed loop system established through the boundedness of transformation and the inverse transformation. Simulation results show that the closed loop system is stable.