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Convergence analysis of first-order discrete multi-agent systems with cooperative-competitive mechanisms

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  • Shi, Lin
  • Gou, Kuixiang
  • Xie, Dongmei

Abstract

This paper focuses on the convergence analysis of first-order discrete multi-agent systems (MASs) with cooperative-competitive mechanisms. Firstly, compared with the existing results, our paper uses the condition of containing a directed spanning to replace that of strong connectivity, and gets a lager range of ε to guarantee that limk→+∞Pk exists, which greatly improves the famous Perron–Frobenius theorem in Olfati-Saber et al. (2007)[24]. Subsequently, we can divide all the agents into m subgroups according to the actual demand, and give the design method of weights so that system can achieve different consensus. We further generalize the results from first-order MASs to second-order MASs. Finally, numerical examples are given to verify the effectiveness of our results.

Suggested Citation

  • Shi, Lin & Gou, Kuixiang & Xie, Dongmei, 2021. "Convergence analysis of first-order discrete multi-agent systems with cooperative-competitive mechanisms," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005518
    DOI: 10.1016/j.amc.2021.126462
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    References listed on IDEAS

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    1. Wu, Jie & Deng, Qun & Han, Tao & Yang, Qing-Sheng & Zhan, Heng, 2019. "Bipartite tracking consensus for multi-agent systems with Lipschitz-Type nonlinear dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1360-1369.
    2. Kaviarasan, Boomipalagan & Kwon, Oh-Min & Park, Myeong Jin & Sakthivel, Rathinasamy, 2021. "Stochastic faulty estimator-based non-fragile tracking controller for multi-agent systems with communication delay," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. Yilun Shang, 2015. "Group consensus of multi-agent systems in directed networks with noises and time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(14), pages 2481-2492, October.
    4. Zhang, Xuxi & Liu, Xianping & Lewis, Frank L. & Wang, Xia, 2020. "Bipartite tracking consensus of nonlinear multi-agent systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
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