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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 357931, 7 pages
http://dx.doi.org/10.1155/2013/357931
Research Article

An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems

1Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran
2Department of Mathematics, Universiti Putra Malaysia (UPM), 43400 Serdang, Malaysia
3Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

Received 10 March 2013; Accepted 30 July 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

This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called linear combination property of intervals. After this stage, the linearized dynamical system is transformed into a multi domain dynamical system via computational interval partitioning. Moreover, the integral form of this multidomain dynamical system is considered. Collocating these constraints at the Legendre Gauss Lobatto (LGL) points together with using the Legendre Gauss Lobatto quadrature rule for approximating the involved integrals enables us to transform the basic OCPs into the associated nonlinear programming problems (NLPs). In all parts of this procedure, the associated control and state functions are approximated by piecewise constants and piecewise polynomials, respectively. An illustrative example is provided for confirming the accuracy and applicability of the proposed idea.