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2013 An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems
Emran Tohidi, Atena Pasban, A. Kilicman, S. Lotfi Noghabi
Abstr. Appl. Anal. 2013(SI50): 1-7 (2013). DOI: 10.1155/2013/357931

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.

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Emran Tohidi. Atena Pasban. A. Kilicman. S. Lotfi Noghabi. "An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems." Abstr. Appl. Anal. 2013 (SI50) 1 - 7, 2013. https://doi.org/10.1155/2013/357931

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1291.49020
MathSciNet: MR3102723
Digital Object Identifier: 10.1155/2013/357931

Rights: Copyright © 2013 Hindawi

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