## Abstract and Applied Analysis

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 240352, 8 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512007

Digital Object Identifier
doi:10.1155/2013/240352

Mathematical Reviews number (MathSciNet)
MR3093751

Zentralblatt MATH identifier
1291.93253

#### Citation

Swaidan, Waleeda; Hussin, Amran. Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems. Abstr. Appl. Anal. 2013 (2013), Article ID 240352, 8 pages. doi:10.1155/2013/240352. https://projecteuclid.org/euclid.aaa/1393512007

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