The Iterative Method for Optimal Control Problems by the Shifted Legendre Polynomials

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Volume 11, Issue 2

A. Ordookhani and H. Kharazi

J. Info. Comput. Sci. , 11 (2016), pp. 120-128.

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Abstract

In this paper an iterative method based on shifted Legendre polynomials is presented to obtain the approximate solutions of optimal control problems subject to integral equations. The operational matrices of integration and product of shifted Legendre polynomials for solving integral equation is employed. The methodology is based on the parametrization of control and state functions. This converted the problem to nonlinear optimization problem in any iteration. In addition, some numerical examples are presented to illustrate the accuracy and efficiency of the proposed method.

Keywords

Optimal control problem, Legendre polynomials, Iterative method.

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@Article{JICS-11-120, author = {A. Ordookhani and H. Kharazi}, title = {The Iterative Method for Optimal Control Problems by the Shifted Legendre Polynomials}, journal = {Journal of Information and Computing Science}, year = {2016}, volume = {11}, number = {2}, pages = {120--128}, abstract = {In this paper an iterative method based on shifted Legendre polynomials is presented to obtain the approximate solutions of optimal control problems subject to integral equations. The operational matrices of integration and product of shifted Legendre polynomials for solving integral equation is employed. The methodology is based on the parametrization of control and state functions. This converted the problem to nonlinear optimization problem in any iteration. In addition, some numerical examples are presented to illustrate the accuracy and efficiency of the proposed method. }, issn = {3080-180X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22520.html} }

TY - JOUR T1 - The Iterative Method for Optimal Control Problems by the Shifted Legendre Polynomials AU - A. Ordookhani and H. Kharazi JO - Journal of Information and Computing Science VL - 2 SP - 120 EP - 128 PY - 2016 DA - 2016/06 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jics/22520.html KW - Optimal control problem, Legendre polynomials, Iterative method. AB - In this paper an iterative method based on shifted Legendre polynomials is presented to obtain the approximate solutions of optimal control problems subject to integral equations. The operational matrices of integration and product of shifted Legendre polynomials for solving integral equation is employed. The methodology is based on the parametrization of control and state functions. This converted the problem to nonlinear optimization problem in any iteration. In addition, some numerical examples are presented to illustrate the accuracy and efficiency of the proposed method.

A. Ordookhani and H. Kharazi. (2016). The Iterative Method for Optimal Control Problems by the Shifted Legendre Polynomials. Journal of Information and Computing Science. 11 (2). 120-128. doi:

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