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

Abstract

This paper elaborated an effective and robust metaheuristic algorithm withacceptable performance based on solution accuracy. The algorithm applied insolution of the optimal control of fractional Volterra integro-differential (FVID)equation which be substituted by nonlinear programming (NLP). Subsequentlythe FIVD convert the problem to a NLP by using spectral collocation tech-niques and thereafter we execute the grey wolf optimizer (GWO) to improvethe speed and accuracy and find the solutions of the optimal control and stateas well as the optimal value of the cost function. It is mentioned that theutilization of the GWO is simple, due to the fact that the GWO is globalsearch algorithm, the method can be applied to find optimal solution of theNLP. The efficiency of the proposed scheme is shown by the results obtained incomparison with the local methods. Further, some illustrative examples intro-duced with their approximate solutions and the results of the present approachcompared with those achieved using other methods.