An Integrated Multicriterionhp-Adaptive Pseudospectral Method for Direct Optimal Control Problems Solving

Abstract

Pseudospectral methods (PMs) for solving general optimal control problems (OCPs) attract an increasing amount of research and application in engineering. It is challenging to improve the convergence rate, the solution accuracy, and the applicability of PMs, especially for nonsmooth problems. Existinghp-adaptive PMs consider only one heuristic criterion, which cannot produce satisfactory performance in many cases. In this paper, we propose a novel method which integrates multicriterion tohp-adaptive PM, in order to further improve the performance. For this purpose, we first devise an OCP solving framework ofhp-adaptive PM. We then design a multicriterionhp-adaptive strategy which introduces prior knowledge, intermediate error and curvature as useful criterions for adaptive refinement. We last present an iterative procedure for solving general nonlinear OCPs. Results from two examples show that our method significantly outperforms competitors on the convergence rate and the solution accuracy. The method is practical and effective for direct solving of various OCPs in a broad range of engineering.