Receding horizon control for nonlinear parabolic partial differential equations with boundary control inputs

Optimal control of nonlinear partial differential equations (PDEs) is an open problem with applications that include fluid, thermal, biological, and chemically-reacting systems. Receding horizon control with the continuation/ generalized minimum residual (C/GMRES) method is a fast algorithm to solve the optimal control problem of nonlinear systems described by ordinary differential equations. In this paper, we develop a design method of the receding horizon control for nonlinear systems described by partial differential equations. Our approach is a direct infinite dimensional extension of the receding horizon control method for finite-dimensional systems. In this paper, we moreover propose an efficient algorithm rather than the C/GMRES algorithm for numerically solving the nonlinear receding horizon control problem. The effectiveness of the proposed method is verified by numerical simulations.