Research Article Open Access

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

Mohammad Ali Tavallaei1 and Behrouz Tousi1
  • 1 ,
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

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.

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Keywords

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