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ISSN: 1941-7020 (Print)
ISSN: 1941-7039 (Online)
Research Article Open Access

Closed Form Solution to an Optimal Control Problem by Orthogonal Polynomial Expansion

Mohammad Ali Tavallaei1 and Behrouz Tousi1
  • 1 Urmia University, Iran

Abstract

In this study the use of orthogonal polynomials for obtaining a close form solution to optimal control problems with a weighed quadratic cost function, is proposed. The method consists of using the Orthogonal Polynomials for the expansion of the state variables and the control signal. This expansion results in a set of linear equations, from which the closed form solution is obtained. A numerical example is provided to demonstrate the applicability and effectiveness of the proposed method.

American Journal of Engineering and Applied Sciences
Volume 1 No. 2, 2008, 104-109

DOI: https://doi.org/10.3844/ajeassp.2008.104.109

Submitted On: 7 May 2008 Published On: 30 June 2008

How to Cite: Tavallaei, M. A. & Tousi, B. (2008). Closed Form Solution to an Optimal Control Problem by Orthogonal Polynomial Expansion . American Journal of Engineering and Applied Sciences, 1(2), 104-109. https://doi.org/10.3844/ajeassp.2008.104.109

Open AccessCopyright: © 2008 Mohammad Ali Tavallaei and Behrouz Tousi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Optimal control
  • orthogonal polynomials
  • spectral method
  • legendry polynomials
  • riccati method