Metaheuristic methods to identify parameters and orders of fractional-order chaotic systems

Abstract

For the synchronization and control of fractional-order chaotic systems, knowing parameters and orders is essential as well as being a hot topic. In this paper, the problem of parameters and orders identification is transformed into a multidimensional optimization problem. Five of the latest metaheuristic methods are employed to solve the parameter identification problem for six fractional-order chaotic systems. These metaheuristic methods involve Ali Baba and the Forty Thieves (AFT), Chameleon Swarm (CS) method, Artificial Gorilla Troops (AGT) Optimizer, Coot Bird (CB), and Harris Hawks (HH) optimization. Three novel fractional-order chaotic systems, in addition to Borah, Chen, and financial systems, are investigated. The Mean Square Error is used as an objective function to find the optimal parameters and orders of fractional-order chaotic systems. Numerical simulations demonstrate that the Ali Baba and the Forty Thieves (AFT) method achieves greater accuracy with a higher convergence rate for parameter identification problem for four selected fractional-order chaotic systems, while the Artificial Gorilla Troops (AGT) optimizer obtains better numerical and graphical results for two fractional-order chaotic systems compared to other metaheuristic methods.