Communications on Pure and Applied Analysis (CPAA)

Solution of nonlinear delay optimal control problems using a composite pseudospectral collocation method

Pages: 1379 - 1389, Volume 9, Issue 5, September 2010      doi:10.3934/cpaa.2010.9.1379

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Hamid Reza Marzban - Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 8415683111, Iran (email)
Hamid Reza Tabrizidooz - Department of Mathematics, Faculty of Science, University of Kashan, Kashan, 8731751167, Iran (email)

Abstract: We develop a composite collocation approximation scheme for the numerical solution of nonlinear delay optimal control problems. For this purpose, we present an extension and also modification for the Gauss pseudospectral method using the hybrid of block-pulse functions and Lagrange polynomials based on the Legendre-Gauss points. In this respect, we derive the corresponding operational matrix of derivative according to the weak representation of derivative operator. In order to demonstrate the applicability, efficiency and accuracy of the proposed method, we examine two illustrative examples.

Keywords:  Delay optimal control problems, Lagrange polynomials, hybrid functions, pseudospectral methods.
Mathematics Subject Classification:  Primary: 49M25; Secondary: 65D25, 65M70.

Received: September 2009;      Revised: January 2010;      Available Online: May 2010.