An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications

In this paper, an efficient computation method is developed for solving a general class of minmax optimal control problems, where the minimum deviation from the violation of the continuous state inequality constraints is maximized. The constraint transcription method is used to construct a smooth ap...

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Bibliographic Details
Main Authors:	Li, Bin, Teo, Kok Lay, Zhao, G., Duan, G.
Format:	Journal Article
Published:	Cambridge University Press 2009
Subjects:	minmax optimal control windshear downburst aircraft abort landing obstacle avoidance root finding control parametrization constraint transcription time scaling transform computation method continuous state inequality constraints
Online Access:	http://hdl.handle.net/20.500.11937/21706

id	curtin-20.500.11937-21706
recordtype	eprints
spelling	curtin-20.500.11937-217062017-09-13T15:57:06Z An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications Li, Bin Teo, Kok Lay Zhao, G. Duan, G. minmax optimal control windshear downburst aircraft abort landing obstacle avoidance root finding control parametrization constraint transcription time scaling transform computation method continuous state inequality constraints In this paper, an efficient computation method is developed for solving a general class of minmax optimal control problems, where the minimum deviation from the violation of the continuous state inequality constraints is maximized. The constraint transcription method is used to construct a smooth approximate function for each of the continuous state inequality constraints. We then obtain an approximate optimal control problem with the integral of the summation of these smooth approximate functions as its cost function. A necessary condition and a sufficient condition are derived showing the relationship between the original problem and the smooth approximate problem. We then construct a violation function from the solution of the smooth approximate optimal control problem and the original continuous state inequality constraints in such a way that the optimal control of the minmax problem is equivalent to the largest root of the violation function, and hence can be solved by the bisection search method. The control parametrization and a time scaling transform are applied to these optimal control problems. We then consider two practical problems: the obstacle avoidance optimal control problem and the abort landing of an aircraft in a windshear downburst. 2009 Journal Article http://hdl.handle.net/20.500.11937/21706 10.1017/S1446181110000040 Cambridge University Press fulltext
repository_type	Digital Repository
institution_category	Local University
institution	Curtin University Malaysia
building	Curtin Institutional Repository
collection	Online Access
topic	minmax optimal control windshear downburst aircraft abort landing obstacle avoidance root finding control parametrization constraint transcription time scaling transform computation method continuous state inequality constraints
spellingShingle	minmax optimal control windshear downburst aircraft abort landing obstacle avoidance root finding control parametrization constraint transcription time scaling transform computation method continuous state inequality constraints Li, Bin Teo, Kok Lay Zhao, G. Duan, G. An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications
description	In this paper, an efficient computation method is developed for solving a general class of minmax optimal control problems, where the minimum deviation from the violation of the continuous state inequality constraints is maximized. The constraint transcription method is used to construct a smooth approximate function for each of the continuous state inequality constraints. We then obtain an approximate optimal control problem with the integral of the summation of these smooth approximate functions as its cost function. A necessary condition and a sufficient condition are derived showing the relationship between the original problem and the smooth approximate problem. We then construct a violation function from the solution of the smooth approximate optimal control problem and the original continuous state inequality constraints in such a way that the optimal control of the minmax problem is equivalent to the largest root of the violation function, and hence can be solved by the bisection search method. The control parametrization and a time scaling transform are applied to these optimal control problems. We then consider two practical problems: the obstacle avoidance optimal control problem and the abort landing of an aircraft in a windshear downburst.
format	Journal Article
author	Li, Bin Teo, Kok Lay Zhao, G. Duan, G.
author_facet	Li, Bin Teo, Kok Lay Zhao, G. Duan, G.
author_sort	Li, Bin
title	An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications
title_short	An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications
title_full	An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications
title_fullStr	An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications
title_full_unstemmed	An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications
title_sort	efficient computational approach to a class of minmax optimal control problems with applications
publisher	Cambridge University Press
publishDate	2009
url	http://hdl.handle.net/20.500.11937/21706
first_indexed	2018-09-06T20:21:09Z
last_indexed	2018-09-06T20:21:09Z
_version_	1610890891058216960

An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications

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