An integrated multicriterion \(hp\)-adaptive pseudospectral method for direct optimal control problems solving
type: Item
instance of: scholarly article
title: An integrated multicriterion \(hp\)-adaptive pseudospectral method for direct optimal control problems solving
zbMATH Open document ID: 1264.65125
DOI: 10.1155/2012/760890
author: Hongfu Liu
author: Shaofei Chen
author: Lincheng Shen
author: Jing Chen
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: 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 in many cases. In this paper, we propose a novel method which 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 \(hp\)-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.
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 49M25
zbMATH DE Number: 6173555
Wikidata QID: Q58911796
describes a project that uses: SNOPT
describes a project that uses: GPOPS
describes a project that uses: TOMLAB
describes a project that uses: SOCS
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/760890
OpenAlex ID: W2112185637
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description: scientific article; zbMATH DE number 6173555