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Finite-time Asymmetric Bipartite Consensus for Signed Networks of Dynamic Agents

  • Xing Guo
  • Jinling LiangEmail author
  • Jianquan Lu
Article
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Abstract

This paper addresses the finite-time asymmetric bipartite consensus problem for multi-agent systems (MAS) associated with signed graphs. Different from bipartite consensus in the previous literatures, asymmetric bipartite consensus means that the states of all agents will converge to two values with different signs and modulus. Two distinct nonlinear consensus control protocols are constructed for the considered system to achieve the finite-time asymmetric bipartite consensus and the fixed-time asymmetric bipartite consensus, respectively. Under the first proposed protocol, it is shown that within a finite time, the considered system can realize asymmetric bipartite consensus. To strengthen the obtained result, the second protocol is proposed, which guarantees that all agents could achieve the asymmetric bipartite consensus in fixed time, that is, the finite-time consensus can be reached before a settling time which is irrelevant with the initial states of the agents. Finally, numerical simulations are given to verify effectiveness of the proposed consensus control protocols.

Keywords

Asymmetric bipartite consensus finite-time convergence fixed-time consensus multi-agent systems signed graphs 

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References

  1. [1]
    Y. U. Cao, A. S. Fukunaga, and A. B. Kahng, “Cooperative mobile robotics: antecedents and directions,” Autonomous Robots, vol. 4, no. 1, pp. 7–27, 1997.Google Scholar
  2. [2]
    M. Mucientes and J. Casillas, “Quick design of fuzzy controllers with good interpretability in mobile robotics,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 4, pp. 636–651, 2007.Google Scholar
  3. [3]
    M. Al Khawaldah, M. Al-Khedher, I. Al-Adwan, and A. Al Rawashdeh, “An autonomous exploration strategy for cooperative mobile robots,” Journal of Software Engineering and Applications, vol. 7, no. 3, pp. 142–149, 2014.Google Scholar
  4. [4]
    C. Florens, M. Franceschetti, and R. J. McEliece, “Lower bounds on data collection time in sensory networks,” IEEE Journal on Selected Areas in Communications, vol. 22, no. 6, pp. 1110–1120, 2004.Google Scholar
  5. [5]
    I. D. Couzin, “Sensory networks and distributed cognition in animal groups,” Proceedings of the 13th International Conference on Autonomous Agents and Multiagent Systems, May 5–9, 2014 Paris, France. pp. 1–2, 2014.Google Scholar
  6. [6]
    D. Yan, J. Cheng, Y. Lu, and W. Ng, “Blogel: a blockcentric framework for distributed computation on realworld graphs,” Proceedings of the VLDB Endowment, vol. 7, no. 14, pp. 1981–1992, 2014.Google Scholar
  7. [7]
    U. Bauer, M. Kerber, and J. Reininghaus, “Distributed computation of persistent homology,” Proceedings of the Meeting on Algorithm Engineering & Experiments, January 5, 2014. Portland, Oregon, USA. pp. 31–38, 2014.Google Scholar
  8. [8]
    J. Wang, K. Liang, X. Huang, Z. Wang, and H. Shen, “Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback,” Applied Mathematics and Computation, vol. 328, pp. 247–262, 2018.MathSciNetGoogle Scholar
  9. [9]
    J. Lu, D. W. C. Ho, and L. Wu, “Exponential stabilization of switched stochastic dynamical networks,” Nonlinearity, vol. 22, pp. 889–911, 2009.MathSciNetzbMATHGoogle Scholar
  10. [10]
    J.Wang, J. Liang, and A. M. Dobaie, “Controller synthesis for switched T-S fuzzy positive systems described by the Fornasini-Marchesini second model,” Nonlinear Analysis: Hybrid Systems, vol. 29, pp. 247–260, 2018.MathSciNetzbMATHGoogle Scholar
  11. [11]
    Y. Wang, J. Lu, J. Liang, J. Cao, and M. Perc, “Pinning synchronization of nonlinear coupled Lur’e networks under hybrid impulses,” IEEE Transactions on Circuits and Systems-II: Express Briefs, doi:10.1109/TCSII.2018.2844883Google Scholar
  12. [12]
    X. Chen, J. Cao, J. H. Park, T. Huang, and J. Qiu, “Finitetime multi-switching synchronization behavior for multiple chaotic systems with network transmission mode,” Journal of the Franklin Institute, vol. 355, no. 5, pp. 2892–2911, 2018.MathSciNetzbMATHGoogle Scholar
  13. [13]
    R. Olfati-Saber, “Flocking for multi-agent dynamic systems: algorithms and theory,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401–420, 2006.MathSciNetzbMATHGoogle Scholar
  14. [14]
    H. Su, X. Wang, and Z. Lin, “Flocking of multi-agents with a virtual leader,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 293–307, 2009.MathSciNetzbMATHGoogle Scholar
  15. [15]
    K. Saulnier, D. Saldaña, A. Prorok, G. J. Pappas, and V. Kumar, “Resilient flocking for mobile robot teams,” IEEE Robotics and Automation Letters, vol. 2, no. 2, pp. 1039–1046, 2017.Google Scholar
  16. [16]
    P.-P. Li, D.-F. Zheng, and P. M. Hui, “Dynamics of opinion formation in a small-world network,” Physical Review E, vol. 73, no. 5, p. 0561.8, 2006.Google Scholar
  17. [17]
    C. Altafini, “Dynamics of opinion forming in structurally balanced social networks,” PloS One, vol. 7, no. 6, p. e38135, 2012.Google Scholar
  18. [18]
    B. O. Baumgaertner, R. C. Tyson, and S. M. Krone, “Opinion strength influences the spatial dynamics of opinion formation,” The Journal of Mathematical Sociology, vol. 40, no. 4, pp. 207–218, 2016.MathSciNetGoogle Scholar
  19. [19]
    R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multi-agent systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 215–233, 2007.zbMATHGoogle Scholar
  20. [20]
    Y. Cao, W. Yu, W. Ren, and G. Chen, “An overview of recent progress in the study of distributed multi-agent coordination,” IEEE Transactions on Industrial Informatics, vol. 9, no. 1, pp. 427–438, 2013.Google Scholar
  21. [21]
    L. Li, D. W. C. Ho, and J. Lu, “Event-based network consensus with communication delays,” Nonlinear Dynamics, vol. 87, no. 3, pp. 1847–1858, 2017.zbMATHGoogle Scholar
  22. [22]
    L. Wang and F. Xiao, “Finite-time consensus problems for networks of dynamic agents,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 950–955, 2010.MathSciNetzbMATHGoogle Scholar
  23. [23]
    H. Shen, F. Li, H. Yan, H. R. Karimi, and H.-K. Lam, “Finite-time event-triggered H¥ control for T-S fuzzy Markov jump systems,” IEEE Transactions Fuzzy Systems, vol. 26, no. 5, pp. 3122–3135, 2018Google Scholar
  24. [24]
    H. Shen, M. Xing, S. Huo, Z. Wu, and J. H. Park, “Finitetime H¥ asynchronous state estimation for discrete-time fuzzy markov jump neural networks with uncertain measurements,” Fuzzy Sets Systems, vol. 356, pp. 113–128, 2019.MathSciNetGoogle Scholar
  25. [25]
    H. Li, X. Liao, and G. Chen, Leader-following finite-time consensus in second-order multi-agent networks with nonlinear dynamics, International Journal of Control, Automation, and Systems, vol. 11, no. 2, pp. 422–426, 2013.Google Scholar
  26. [26]
    Y. Shang, “Finite-time cluster average consensus for networks via distributed iterations,” International Journal of Control, Automation, and Systems, vol. 15, no. 2, pp. 933–938, 2017.Google Scholar
  27. [27]
    S. Li, H. Du, and X. Lin, “Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics,” Automatica, vol. 47, no. 8, pp. 1706–1712, 2011.MathSciNetzbMATHGoogle Scholar
  28. [28]
    X. Wang and Y. Hong, “Finite-time consensus for multiagent networks with second-order agent dynamics,” IFAC Proceedings Volumes, vol. 41, no. 2, pp. 15185–15190, 2008.Google Scholar
  29. [29]
    Q. Hui, W. M. Haddad, and S. P. Bhat, “Finite-time semistability and consensus for nonlinear dynamical networks,” IEEE Transactions on Automatic Control, vol. 53, no. 8, pp. 1887–1900, 2008.MathSciNetzbMATHGoogle Scholar
  30. [30]
    X. Li, X. Luo, J. Wang, and X. Guan, “Finite-time consensus of nonlinear multi-agent system with prescribed performance,” Nonlinear Dynamics, vol. 91, no. 4, pp. 2397–2409, 2018.zbMATHGoogle Scholar
  31. [31]
    Y. Huang and Y. Jia, “Fixed-time consensus tracking control of second-order multi-agent systems with inherent nonlinear dynamics via output feedback,” Nonlinear Dynamics, vol. 91, no. 2, pp. 1289–1306, 2018.zbMATHGoogle Scholar
  32. [32]
    X. Guo, J. Liang, and J. Lu, “Asymmetric bipartite consensus over directed networks with antagonistic interactions,” IET Control Theory & Applications, vol. 12, no. 17, p. 2295. 2018.Google Scholar
  33. [33]
    S. Sundaram and C. N. Hadjicostis, “Finite-time distributed consensus in graphs with time-invariant topologies,” in Proceedings of the 2007.American Control Conference, July 11–13, 2007. New York City, USA. pp. 711–716, 2007.Google Scholar
  34. [34]
    S. E. Parsegov, A. E. Polyakov, and P. S. Shcherbakov, “Fixed-time consensus algorithm for multi-agent systems with integrator dynamics,” IFAC Proceedings Volumes, vol. 46, no. 27, pp. 110–115, 2013.Google Scholar
  35. [35]
    M. Defoort, A. Polyakov, G. Demesure, M. Djemai, and K. Veluvolu, “Leader-follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics,” IET Control Theory & Applications, vol. 9, no. 14, pp. 2165–2170, 2015.MathSciNetGoogle Scholar
  36. [36]
    Z. Zuo and L. Tie, “Distributed robust finite-time nonlinear consensus protocols for multi-agent systems,” International Journal of Systems Science, vol. 47, no. 6, pp. 1366–1375, 2016.MathSciNetzbMATHGoogle Scholar
  37. [37]
    L. Zhao, Y. Jia, and J. Du, “Adaptive finite-time bipartite consensus for second-order multi-agent systems with antagonistic interactions,” Systems & Control Letters, vol. 102, pp. 22–31, 2017.MathSciNetzbMATHGoogle Scholar
  38. [38]
    C. Altafini, “Consensus problems on networks with antagonistic interactions,” IEEE Transactions on Automatic Control, vol. 58, no. 4, pp. 935–946, 2013.MathSciNetzbMATHGoogle Scholar
  39. [39]
    J. Hu and W. X. Zheng, “Bipartite consensus for multiagent systems on directed signed networks,” in Proc. of 52nd IEEE Conference on Decision and Control, Florence, Italy, pp. 3451–3456, December 10–13, 2013.Google Scholar
  40. [40]
    M. E. Valcher and P. Misra, “On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions,” Systems & Control Letters, vol. 66, pp. 94–103, 2014.MathSciNetzbMATHGoogle Scholar
  41. [41]
    H. Zhang and J. Chen, “Bipartite consensus of general linear multi-agent systems,” Proc. of American Control Conference, June 4-6, 2014. Portland, Oregon, USA. pp. 808–812, 2014.Google Scholar
  42. [42]
    D. Meng, Y. Jia, and J. Du, “Finite-time consensus for multiagent systems with cooperative and antagonistic interactions,” IEEE Transactions on Neural Networks and Learning Systems, vol. 27, no. 4, pp. 762–770, 2016.MathSciNetGoogle Scholar
  43. [43]
    A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106–2110, 2012.MathSciNetzbMATHGoogle Scholar
  44. [44]
    W. Ren and R.W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 655–661, 2005.MathSciNetzbMATHGoogle Scholar
  45. [45]
    R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, England, 1990.zbMATHGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.School of Information Science and EngineeringSoutheast UniversityNanjingChina
  2. 2.School of MathematicsSoutheast UniversityNanjingChina

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