Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 760890, 22 pages
Research Article

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

College of Mechatronic Engineering and Automation, National University of Defense Technology, Hunan Province, Changsha 410073, China

Received 4 July 2012; Revised 5 October 2012; Accepted 6 October 2012

Academic Editor: Ming Li

Copyright © 2012 Hongfu Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 -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 to -adaptive PM, in order to further improve the performance. For this purpose, we first devise an OCP solving framework of -adaptive PM. We then design a multicriterion -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.