Receding Horizon Control for High-Dimensional Burgers' Equations with Boundary Control Inputs

Receding horizon control is a feedback control approach that optimizes control performance over a finite horizon, and its performance index has moving initial and terminal times. Controlling the flow of fluids is a challenging problem that arises in many fields including aeronautical, biological and chemical engineering. The objective of this study is to provide a novel framework for designing a receding horizon controller for high-dimensional Burgers' equations used to describe fundamental flow phenomena. The advantage of our proposed method is that it can be applied to a wide class of optimization problems of high-dimensional Burgers' equations. The effectiveness of the proposed method is verified by numerical simulation.