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Different types of sliding mode controller for nonlinear fractional multi-Agent system

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  • Sharafian, Amin
  • Sharifi, Alireza
  • Zhang, Weidong

Abstract

In this article, five particular types of sliding surfaces are presented to overcome consensus tracking problem for a class of nonlinear fractional multi-agent systems. Meanwhile, the sliding mode controller is suggested due to the presence of external disturbances in the follower agents dynamic models, the robust disturbance rejection control input can stabilize the consensus error dynamic of the fractional multi-agent system. Hence, both integer and fractional-order sliding surfaces are applied to increase the accuracy and convergence speed. The stabilities of various sliding surfaces are proved based on Lyapunov direct strategy and also Mittag-Leffler stability for fractional derivations. In this note it is assumed that the exact knowledge of the leader-follower dynamic, upper bound of smooth disturbance, full state access, and delay free communication among agents are available. In order to show the sliding motion accrues in finite time, upper bounds for reaching times of sliding surfaces are obtained. Moreover, based on the principle of dynamic memory resetting of fractional operators it is forced an invariant finite time sliding mode. Ultimately, the simulation results on the Arneodo chaotic system shows the capability of the proposed method.

Suggested Citation

  • Sharafian, Amin & Sharifi, Alireza & Zhang, Weidong, 2020. "Different types of sliding mode controller for nonlinear fractional multi-Agent system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304278
    DOI: 10.1016/j.chaos.2019.109481
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    References listed on IDEAS

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    1. Tiedong Ma & Teng Li & Bing Cui, 2018. "Coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(1), pages 1-14, January.
    2. A.J. Muñoz-Vázquez & V. Parra-Vega & A. Sánchez-Orta, 2017. "A novel continuous fractional sliding mode control," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(13), pages 2901-2908, October.
    3. Huang, Chengdai & Cao, Jinde, 2017. "Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 262-275.
    4. Dariush Khezrimotlagh & Yao Chen, 2018. "The Optimization Approach," International Series in Operations Research & Management Science, in: Decision Making and Performance Evaluation Using Data Envelopment Analysis, chapter 0, pages 107-134, Springer.
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    Cited by:

    1. Ma, Yajing & Li, Zhanjie & Xie, Xiangpeng & Yue, Dong, 2023. "Adaptive consensus of uncertain switched nonlinear multi-agent systems under sensor deception attacks," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Mobayen, Saleh & Alattas, Khalid A. & Fekih, Afef & El-Sousy, Fayez F.M. & Bakouri, Mohsen, 2022. "Barrier function-based adaptive nonsingular sliding mode control of disturbed nonlinear systems: A linear matrix inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Gao, Shanshan & Zhang, Shenggui & Chen, Xinzhuang, 2023. "Effects of changing the weights of arcs on the consensus convergence rate of a leader–follower multi-agent system," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Sharafian, Amin & Kanesan, Jeevan & Khairuddin, Anis Salwa Mohd & Ramanathan, Anand & Sharifi, Alireza & Bai, Xiaoshan, 2023. "A novel approach to state estimation of HIV infection dynamics using fixed-time fractional order observer," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    5. Yin, Xiangxin & Dai, Haifeng & Zhao, Lingzhi & Zhao, Donghua & Xiao, Rui & Sun, Yongzheng, 2024. "Control costs of long-range interacting multi-agent systems with noise perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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