Receding horizon control with numerical solution for spatiotemporal dynamic 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. Spatiotemporal dynamic systems are often described by partial differential equations, and their behavior is characterized by both spatial and temporal variables. In this study, we develop a design method of receding horizon control for a generalized class of spatiotemporal dynamic systems. Using the variational principle, we first derive the exact stationary conditions that must be satisfied for a performance index to be optimized. Next, we provide a numerical algorithm for solving the stationary conditions via finite-dimensional approximation. Finally, the effectiveness of the proposed method is verified by numerical simulations.