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Abstract and Applied Analysis
Volume 2014, Article ID 752854, 12 pages
http://dx.doi.org/10.1155/2014/752854
Research Article

A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints

School of Mathematical Science, Heilongjiang University, Harbin 150080, China

Received 13 December 2013; Accepted 14 April 2014; Published 8 May 2014

Academic Editor: Gaston M. N’Guérékata

Copyright © 2014 Xiangyu Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider an optimal control problem subject to the terminal state equality constraint and continuous inequality constraints on the control and the state. By using the control parametrization method used in conjunction with a time scaling transform, the constrained optimal control problem is approximated by an optimal parameter selection problem with the terminal state equality constraint and continuous inequality constraints on the control and the state. On this basis, a simple exact penalty function method is used to transform the constrained optimal parameter selection problem into a sequence of approximate unconstrained optimal control problems. It is shown that, if the penalty parameter is sufficiently large, the locally optimal solutions of these approximate unconstrained optimal control problems converge to the solution of the original optimal control problem. Finally, numerical simulations on two examples demonstrate the effectiveness of the proposed method.