Control parameterization for optimal control problems with continuous inequality constraints: New       convergence results

Ryan Loxton; Qun Lin; Volker Rehbock; Kok Lay Teo

doi:10.3934/naco.2012.2.571

Article Contents

2012, Volume 2, Issue 3: 571-599. Doi: 10.3934/naco.2012.2.571

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Control parameterization for optimal control problems with continuous inequality constraints: New convergence results

1.
Department of Mathematics and Statistics, Curtin University, GPO Box U1987 Perth, Western Australia 6845
2.
Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, Western Australia 6845

Received: March 2012

Revised: May 2012

Published: July 2012

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Abstract

Control parameterization is a powerful numerical technique for solving optimal control problems with general nonlinear constraints. The main idea of control parameterization is to discretize the control space by approximating the control by a piecewise-constant or piecewise-linear function, thereby yielding an approximate nonlinear programming problem. This approximate problem can then be solved using standard gradient-based optimization techniques. In this paper, we consider the control parameterization method for a class of optimal control problems in which the admissible controls are functions of bounded variation and the state and control are subject to continuous inequality constraints. We show that control parameterization generates a sequence of suboptimal controls whose costs converge to the true optimal cost. This result has previously only been proved for the case when the admissible controls are restricted to piecewise continuous functions.

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Mathematics Subject Classification: Primary: 65P99, 93C15; Secondary: 49M37.

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