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

An International Journal of Optimization and Control: Theories & Applications

article

Raheleh Khanduzi¹  Asyieh Ebrahimzadeh²  Samaneh Panjeh Ali Beik³ 

[1] Department of Mathematics and Statistics, Gonbad Kavous University;School of Basic Sciences, Farhangian University;Young Researchers and Elite Club, North Tehran Branch, Islamic Azad University

关键词: Optimal control;    Fractional Volterra integro-differential equation;    collocation method;    Grey wolf optimizer;   

DOI  :  10.11121/ijocta.01.2020.00753

学科分类：地球科学(综合)

来源: Balikesir University

【 摘 要 】

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.

【 授权许可】

CC BY