Compensating for order variation in mesh refinement for direct transcription methods
type: Item
instance of: scholarly article
title: Compensating for order variation in mesh refinement for direct transcription methods
zbMATH Open document ID: 0971.65075
DOI: 10.1016/S0377-0427(00)00465-9
author: J. T. Betts
author: N. Biehn
author: William P. Huffman
author: Stephen L. Campbell
published in: Journal of Computational and Applied Mathematics
publication date: 2001-10-26T00:00:00Z
review text: When implicit Runge-Kutta methods are applied to stiff or differential algebraic equations, they may suffer a reduction of order. In the direct transcription approach to optimal control problems, the theory sometimes fails to accurately predict this reduction which may affect mesh refinement algorithms. The authors describe a new mesh refinement algorithm based on dynamically estimating the order reduction at different parts of the considered interval and on different iterations during the optimisation. The new method is demonstrated on a numerical example with fast transients at both ends of the considered interval.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 65L80
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 1566009
zbMATH Keywords: differential algebraic equation
zbMATH Keywords: optimal control
zbMATH Keywords: implicit Runge-Kutta method
zbMATH Keywords: order reduction
zbMATH Keywords: mesh refinement
zbMATH Keywords: direct transcription
zbMATH Keywords: algorithms
zbMATH Keywords: numerical example
describes a project that uses: SOCS
describes a project that uses: OTIS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1566009