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Parameter estimation for chaotic systems via a hybrid flower pollination algorithm

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Abstract

Parameter estimation is a fundamental research issue which has attracted great concern in the control and synchronization of chaotic systems. This problem can be mathematically described as a multi-dimensional continuous optimization problem through constructing an appropriate fitness function, and then solved via meta-heuristic algorithms. A hybrid flower pollination algorithm is proposed in this paper for solving this problem more efficiently. The proposed algorithm well combines the good global exploration ability of the original flower pollination algorithm and the powerful local exploitation ability of the Nelder–Mead simplex method together by integrating these two methods in a very simple way. The experimental results tested on three typical chaotic system parameter estimation problems with three unknown system parameters, including the Lorenz system, the Rossler system, and the Lorenz system under the noise condition, demonstrate that the algorithm can estimate the unknown parameters efficiently and accurately. The comparisons with the basic flower pollination algorithm and some other four reported methods including the quantum particle swarm optimization, the hybrid adaptive cuckoo search optimization algorithm, the oppositional backtracking search optimization algorithm, and the hybrid algorithm combining differential evolution with artificial bee colony suggest that the proposed algorithm is energy efficient and superior. The proposed algorithm can be used as a new and effective choice for parameter estimation of chaotic systems.

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Acknowledgements

The authors sincerely thank the anonymous reviewers for their constructive comments which improved the quality of this manuscript and acknowledge the supports provided by the National Natural Science Foundation of China (Grant No. 51475270).

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Authors and Affiliations

  1. School of Mechanical Engineering, Shandong University, Jinan, 250061, China

    Shuhui Xu, Yong Wang & Xue Liu

  2. Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Shandong University), Ministry of Education, Jinan, 250061, China

    Shuhui Xu, Yong Wang & Xue Liu

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  1. Shuhui Xu
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  2. Yong Wang
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  3. Xue Liu
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Correspondence to Yong Wang.

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Xu, S., Wang, Y. & Liu, X. Parameter estimation for chaotic systems via a hybrid flower pollination algorithm. Neural Comput & Applic 30, 2607–2623 (2018). https://doi.org/10.1007/s00521-017-2890-2

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