Control law in analytic expression of a system coupled by reaction-diffusion equation

摘要

Control design of a coupled ODE-PDE boundary control system is considered in this paper. The PDE is one dimensional reaction-diffusion equation, with constant parameters, actuated at one of the boundaries and coupled to a linear and time-invariant ODE at the opposite boundary. By introducing a two-step backstepping design procedure, analytic solutions of the kernel and vector-valued functions in the backstepping transformations are obtained. Therefore, a boundary control law in analytic expression is constructed for this coupled ODE-PDE control system. (C) 2020 Elsevier B.V. All rights reserved.