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Differential evolution-based parameter estimation and synchronization of heterogeneous uncertain nonlinear delayed fractional-order multi-agent systems with unknown leader

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Abstract

In this paper, under a fixed directed graph, the distributed cooperative synchronization of heterogeneous uncertain nonlinear chaotic delayed fractional-order multi-agent systems (FOMASs) with a leader of bounded unknown input is investigated, where the fractional orders and system parameters are uncertain and the controller gains are heterogeneous due to imperfect implementation. It should be noted that the study is more general by considering the FOMASs with time delays, unknown leader, heterogeneity, and unknown nonlinear dynamics. Firstly, a differential evolution-based parameter estimation method is proposed to identify the uncertain parameters. Then based on the identified parameters, by using the matrix theory, graph theory, fractional derivative inequality, and comparison principle of linear fractional equation with delay, a heterogeneous discontinuous controller is designed to achieve the distributed cooperative synchronization asymptotically. Thirdly, a heterogeneous continuous controller is further constructed to suppress the undesirable chattering behavior, where uniformly ultimately bounded synchronization tracking errors can be achieved and tuned as small as desired. Finally, numerical simulations are provided to validate the effectiveness of the proposed parameter estimation scheme and the designed control algorithms.

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Acknowledgements

This work was supported by China Scholarship Council and the National Natural Science Foundation of China under Grants 61403019 and 61772063 and the Fundamental Research Funds for the Central Universities under Grant 2017JBM067.

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Authors and Affiliations

  1. CRIStAL, UMR CNRS 9189, Centrale Lille, 59651, Villeneuve-d’Ascq, France

    Wei Hu & Ahmed Rahmani

  2. School of Science, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Guoguang Wen & Yongguang Yu

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  1. Wei Hu
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  2. Guoguang Wen
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Correspondence to Guoguang Wen.

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Hu, W., Wen, G., Rahmani, A. et al. Differential evolution-based parameter estimation and synchronization of heterogeneous uncertain nonlinear delayed fractional-order multi-agent systems with unknown leader. Nonlinear Dyn 97, 1087–1105 (2019). https://doi.org/10.1007/s11071-019-05034-1

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