Receding Horizon Control With Numerical Solution for Nonlinear Parabolic Partial Differential Equations

The optimal control of nonlinear partial differential equations (PDEs) is an open problem with applications that include fluid, thermal, biological, and chemical systems. Receding horizon control is a kind of optimal feedback control, and its performance index has a moving initial time and a moving terminal time. In this study, we develop a design method of receding horizon control for systems described by nonlinear parabolic PDEs. The objective of this study is to develop a novel algorithm for numerically solving the receding horizon control problem for nonlinear parabolic PDEs. The effectiveness of the proposed method is verified by numerical simulations.