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A minimum trapping time problem in optimal control theory

Published online by Cambridge University Press:  17 February 2009

M. E. Fisher ,
J. L. Noakes  and
K. L. Teo
K. L. Teo
Affiliation:
Department of Mathematics, The University of Western Australia, Western Australia 6009.
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Abstract

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In this paper we consider a natural extension of the minimum time problem in optimal control theory which we refer to as the minimum trapping time problem. The minimum trapping time problem requires a fixed time interval [0, T], where T is finite. The aim is to determine a control for which the system trajectory not only reaches a specified target in minimum time but also remains trapped within the target until time T. Our aim is to devise a computational procedure for solving the minimum trapping time problem. The computational procedure we adopt uses control parametrisation in which the class of controls is approximated by a class of piecewise constant functions. The problem we are solving is therefore an approximation to the original minimum trapping time problem. Some properties for the approximate problem are then established. These lead to an extremely efficient iterative procedure for calculating the minimum trapping time.

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 1 , July 1990 , pp. 100 - 114
Copyright
Copyright © Australian Mathematical Society 1990

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