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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 535979, 9 pages
http://dx.doi.org/10.1155/2013/535979
Research Article

Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems

1Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran
2Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Malaysia

Received 13 January 2013; Accepted 8 March 2013

Academic Editor: Mustafa Bayram

Copyright © 2013 Emran Tohidi 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

The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs) has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions.