Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 209329, 15 pages
http://dx.doi.org/10.1155/2012/209329
Research Article

Adaptive Method for Solving Optimal Control Problem with State and Control Variables

Louadj Kahina1 and Aidene Mohamed2

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

Received 29 November 2011; Revised 19 April 2012; Accepted 20 April 2012

Academic Editor: Jianming Shi

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.

Abstract

The problem of optimal control with state and control variables is studied. The variables are: a scalar vector 𝑥 and the control 𝑢 ( 𝑡 ) ; these variables are bonded, that is, the right-hand side of the ordinary differential equation contains both state and control variables in a mixed form. For solution of this problem, we used adaptive method and technology of linear programming.