American Institute of Mathematical Sciences

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September  2010, 9(5): 1379-1389. doi: 10.3934/cpaa.2010.9.1379

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

Hamid Reza Marzban 1, and  Hamid Reza Tabrizidooz 2,

1. 

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 8415683111, Iran
2. 

Department of Mathematics, Faculty of Science, University of Kashan, Kashan, 8731751167, Iran

Received  September 2009 Revised  January 2010 Published  May 2010

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: pseudospectral methods., hybrid functions, Lagrange polynomials, Delay optimal control problems.
Mathematics Subject Classification: Primary: 49M25; Secondary: 65D25, 65M7.
Citation: Hamid Reza Marzban, Hamid Reza Tabrizidooz. Solution of nonlinear delay optimal control problems using a composite pseudospectral collocation method. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1379-1389. doi: 10.3934/cpaa.2010.9.1379
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