An improved adaptive hp mesh refinement method in solving optimal control problems - Luo, Changxin; Li, Jiong; Zhou, Chijun; Lei, Humin (Optimal control applications & methods, 2023)
In order to improve the efficiency of the adaptive hp pseudospectral method in solving the optimal control problems, an improved adaptive hp pseudospectral method is proposed in this paper. This method mainly improves the mesh refinement process of the traditional hp pseudospectral method to reduce the number of mesh iterations, so as to achieve the purpose of shortening the solving time. The focus of this method is twofold. Firstly, by judging the position of the sudden change points of control curve, the mesh is refined in advance around them. Secondly, the non‐uniform segmentation iteration is carried out by using the curvature of the system state curve as the criterion. These two points together improve the solving efficiency of the proposed method. Through the convergence analysis and simulation verification, it is shown that the proposed method can effectively solve the optimal control problem, and it is also proved that the proposed method has higher solving efficiency than the traditional adaptive hp pseudospectral method.