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Nonlinearly constrained optimal control problems involving piecewise smooth controls

Published online by Cambridge University Press:  17 February 2009

K. L. Teo ,
K. K. Leong  and
G. J. Goh
K. L. Teo
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands WA 6009.
K. K. Leong
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands WA 6009.
G. J. Goh
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands WA 6009.
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Abstract

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In this paper, we consider a class of optimal control problems involving inequality continuous-state constraints in which the control is piecewise smooth. The requirement for this type of control is more stringent than that for the control considered in standard optimal control problems in which the controls are usually taken as bounded measurable functions. In this paper, we shall show that this class of optimal control problems can easily be transformed into an equivalent class of combined optimal parameter selection and optimal control problems. We shall then use the control parametrisation technique to devise a computational algorithm for solving this equivalent dynamic optimisation problem. Furthermore, convergence analysis will be given to support this numerical approach. For illustration, two nontrivial optimal control problems involving transferring cargo via a container crane will be solved using the proposed approach.

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 2 , October 1990 , pp. 151 - 179
Copyright
Copyright © Australian Mathematical Society 1990

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