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

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. Existing hp-adaptive PMs consider only one heuristic criterion, which cannot produce satisfactory performance inmany cases. In this paper, we propose a novel methodwhich integrates multicriterion to hp-adaptive PM, in order to further improve the performance. For this purpose, we first devise an OCP solving framework of hp-adaptive PM. We then design a multicriterion hpadaptive 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.