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The control parameterization enhancing transform for constrained optimal control problems

Published online by Cambridge University Press:  17 February 2009

K. L. Teo ,
L. S. Jennings ,
H. W. J. Lee  and
V. Rehbock
K. L. Teo
Affiliation:
School of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987 Perth, WA 6845, Australia
L. S. Jennings
Affiliation:
Centre for Applied Dynamics and Optimization, University of Western Australia, WA 6907, Australia
H. W. J. Lee
Affiliation:
Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong, Shatin, Hong Kong
V. Rehbock
Affiliation:
School of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987 Perth, WA 6845, Australia
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Abstract

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Consider a general class of constrained optimal control problems in canonical form. Using the classical control parameterization technique, the time (planning) horizon is partitioned into several subintervals. The control functions are approximated by piecewise constant or piecewise linear functions with pre-fixed switching times. However, if the optimal control functions to be obtained are piecewise continuous, the accuracy of this approximation process greatly depends on how fine the partition is. On the other hand, the performance of any optimization algorithm used is limited by the number of decision variables of the problem. Thus, the time horizon cannot be partitioned into arbitrarily many subintervals to reach the desired accuracy. To overcome this difficulty, the switching points should also be taken as decision variables. This is the main motivation of the paper. A novel transform, to be referred to as the control parameterization enhancing transform, is introduced to convert approximate optimal control problems with variable switching times into equivalent standard optimal control problems involving piecewise constant or piecewise linear control functions with pre-fixed switching times. The transformed problems are essentially optimal parameter selection problems and hence are solvable by various existing algorithms. For illustration, two non-trivial numerical examples are solved using the proposed method.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 3 , January 1999 , pp. 314 - 335
Copyright
Copyright © Australian Mathematical Society 1999

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