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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 240352, 8 pages
http://dx.doi.org/10.1155/2013/240352
Research Article

Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems

Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 4 April 2013; Revised 27 June 2013; Accepted 1 July 2013

Academic Editor: Shawn X. Wang

Copyright © 2013 Waleeda Swaidan and Amran Hussin. 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

Most of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical technique, which is based on the combination of Haar wavelet collocation method and successive Generalized Hamilton-Jacobi-Bellman equation. We formulate some new Haar wavelet operational matrices in order to manipulate Haar wavelet series. The proposed method has been applied to solve linear and nonlinear optimal control problems with infinite time horizon. The simulation results indicate that the accuracy of the control and cost can be improved by increasing the wavelet resolution.