Parameter identification of fractional-order chaotic systems using different Meta-heuristic Optimization Algorithms

Abstract

Fractional-order chaotic systems (FOCS) parameter identification is an essential issue in chaos control and synchronization process. In this paper, different recent Meta-heuristic Optimization Algorithms are used to estimate the parameters and orders of three FOCS. The investigated systems are Arneodo, Borah rotational attractor and Chen double- and four-wing systems. The employed algorithms are the Salp Swarm Algorithm, Whale Optimization Algorithm, Moth-Flame Optimizer, Grey Wolf Optimizer and the Flower Pollination Algorithm (FPA). The proposed algorithms are applied on several objective functions to identify the FOCS parameters including Mean Square Error (MSE), Integral of Squared Error (ISE), Integral of Absolute Error and Integral of Time Absolute Error. A comparison between the obtained results from each algorithm over each employed objective function is carried out. The target is to investigate the most adequate optimization technique in this difficult multidimensional problem and the best objective function that helps the algorithms capture more accurate and consistent results. The performance of optimization algorithms in the presence of measurement noise has been tested using two objective functions (MSE and ISE) for the three chaotic systems. The overall outcome shows that FPA with ISE objective function is the most efficient combination for the parameter identification of the three FOCS without/with noise because it achieves higher accuracy and more robust results with faster convergence speeds than all other algorithms.

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Correspondence to Lobna A. Said.

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Yousri, D.A., AbdelAty, A.M., Said, L.A. et al. Parameter identification of fractional-order chaotic systems using different Meta-heuristic Optimization Algorithms. Nonlinear Dyn 95, 2491–2542 (2019). https://doi.org/10.1007/s11071-018-4703-2

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Keywords

  • Fractional-order chaotic systems
  • Salp Swarm Algorithm
  • Whale Optimization Algorithm
  • Moth-Flame Optimizer
  • Grey Wolf Optimizer
  • Flower Pollination Algorithm
  • IAE
  • ISE
  • ITAE
  • MSE