Optimal control of fractional integro-differential systems based on a spectral method and grey wolf optimizer

Raheleh Khanduzi; Asyieh Ebrahimzadeh; Samaneh Panjeh Ali Beik

doi:10.11121/ijocta.01.2020.00753

Authors

Raheleh Khanduzi Department of Mathematics and Statistics, Gonbad Kavous University, Golestan, Iran http://orcid.org/0000-0002-0979-4041
Asyieh Ebrahimzadeh School of Basic Sciences, Farhangian University, Tehran, Iran http://orcid.org/0000-0002-4684-7640
Samaneh Panjeh Ali Beik Young Researchers and Elite Club, North Tehran Branch, Islamic Azad University, Tehran, Iran http://orcid.org/0000-0002-6559-3279

DOI:

https://doi.org/10.11121/ijocta.01.2020.00753

Keywords:

Optimal control, Fractional Volterra integro-diﬀerential equation, collocation method, Grey wolf optimizer

Abstract

This paper elaborated an effective and robust metaheuristic algorithm with acceptable performance based on solution accuracy. The algorithm applied in solution of the optimal control of fractional Volterra integro-differential (FVID) equation which be substituted by nonlinear programming (NLP). Subsequently the FIVD convert the problem to a NLP by using spectral collocation techniques and thereafter we execute the grey wolf optimizer (GWO) to improve the speed and accuracy and find the solutions of the optimal control and state as well as the optimal value of the cost function. It is mentioned that the utilization of the GWO is simple, due to the fact that the GWO is global search algorithm, the method can be applied to find optimal solution of the NLP. The efficiency of the proposed scheme is shown by the results obtained in comparison with the local methods. Further, some illustrative examples introduced with their approximate solutions and the results of the present approach compared with those achieved using other methods.

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