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International Journal of Differential Equations
Volume 2012, Article ID 173634, 18 pages
Research Article

Direct Method for Resolution of Optimal Control Problem with Free Initial Condition

1Department of Mathematics, Faculty of Sciences, University Mouloud Mammeri of Tizi-Ouzou, Tizi-Ouzou, Algeria
2Laboratoire de Conception et Conduite de Systèmes de Production (L2CSP), UMMTO Tizi-Ouzou, Algeria

Received 22 September 2011; Accepted 3 November 2011

Academic Editor: Sabri Arik

Copyright © 2012 Louadj Kahina and Aidene Mohamed. 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.


The theory of control analyzes the proprieties of commanded systems. Problems of optimal control (OC) have been intensively investigated in the world literature for over forty years. During this period, series of fundamental results have been obtained, among which should be noted the maximum principle (Pontryagin et al., 1962) and dynamic programming (Bellman, 1963). For many of the problems of the optimal control theory (OCT), adequate solutions are found (Bryson and Yu-chi, 1969, Lee and Markus, 1967, Gabasov and Kirillova, 1977, 1978, 1980). Results of the theory were taken up in various fields of science, engineering, and economics. The present paper aims at extending the constructive methods of Balashevich et al., (2000) that were developed for the problems of optimal control with the bounded initial state is not fixed are considered.