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Optimal control problems with multiple characteristic time points in the objective and constraints

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Open access
Authors
Loxton, Ryan
Teo, Kok Lay
Rehbock, Volker
Date
2008
Type
Journal Article

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Citation
Loxton, R.C. and Teo, K.L. and Rehbock, V. 2008. Optimal control problems with multiple characteristic time points in the objective and constraints. Automatica. 44 (11): pp. 2923-2929.
Source Title
Automatica
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Faculty
School of Science and Computing
Department of Mathematics and Statistics
Faculty of Science and Engineering
Remarks

NOTICE: This is the author’s version of a work that was accepted for publication in Automatica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Automatica, Vol. 44, Issue 11 (2008). doi: 10.1016/j.automatica.2008.04.011

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Abstract

In this paper, we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points. These time points can be either fixed or variable. Using the control parametrization technique and a time scaling transformation, this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems. Each of these approximate problems can be viewed as a finite dimensional optimization problem. New gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be applied to solve each approximate optimal parameter selection problem. For illustration, two numerical examples are solved.