A numerical solution method to receding horizon control for nonlinear diffusion systems

In this paper, we study the optimal control problem of nonlinear parabolic partial differential equations (PDEs) with applications that include fluid and thermal system. Receding horizon control is a kind of optimal feedback control in which the control performance over a finite future is optimized. As described herein, we present a receding horizon control design method for a class of nonlinear parabolic PDEs. Our approach is a direct infinite-dimensional extension of the finite-dimensional receding horizon control method. We also propose a fast algorithm for numerically solving the stationary conditions that must be satisfied for optimality. Results of numerical simulations verified the effectiveness of the proposed method.