Advertisement

Journal of Systems Science and Complexity

, Volume 31, Issue 6, pp 1525–1540 | Cite as

Bipartite Consensus of Discrete-Time Double-Integrator Multi-Agent Systems with Measurement Noise

  • Cuiqin Ma
  • Weiwei Zhao
  • Yunbo Zhao
Article
  • 5 Downloads

Abstract

The effects of measurement noise are investigated in the context of bipartite consensus of multi-agent systems. In the system setting, discrete-time double-integrator dynamics are assumed for the agent, and measurement noise is present for the agent receiving the state information from its neighbors. Time-varying stochastic bipartite consensus protocols are designed in order to lessen the harmful effects of the noise. Consequently, the state transition matrix of the closed-loop system is analyzed, and sufficient and necessary conditions for the proposed protocol to be a mean square bipartite consensus protocol are given with the help of linear transformation and algebraic graph theory. It is proven that the signed digraph to be structurally balanced and having a spanning tree are the weakest communication assumptions for ensuring bipartite consensus. In particular, the proposed protocol is a mean square bipartite average consensus one if the signed digraph is also weight balanced.

Keywords

Bipartite consensus discrete-time double-integrator measurement noise multi-agent systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Olfati-Saber R and Murray R M, Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automatic Control, 2004, 49(9): 1520–1533.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Ren W and Beard R M, Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Trans. Automatic Control, 2005, 50(5): 655–661.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Ma C Q and Zhang J F, Necessary and sufficient conditions for consensusability of linear multiagent systems, IEEE Trans. Automatic Control, 2010, 55(5): 1263–1268.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Ma C Q and Zhang J F, On formability of linear continuous-time multi-agent systems, Journal of Systems Science & Complexity, 2012, 25(1): 13–29.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Sun W, Wang Y, and Yang R, L2 disturbance attenuation for a class of time delay Hamiltonian systems, Journal of Systems Science & Complexity, 2011, 24(4): 672–682.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Wang B C and Zhang J F, Distributed control of large population multiagent systems with random parameters and a major agent, Automatica, 2012, 48(9): 2093–2106.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Aronson E, Wilson T, and Akert R, Social Psychology, Prentice Hall, Upper Saddle River, N. J., 2010.Google Scholar
  8. [8]
    Easley D and Kleinberg J, Networks, Crowds, and Markets, Reasoning About a Highly Connected World, Cambridge University Press, Cambridge, 2010.CrossRefzbMATHGoogle Scholar
  9. [9]
    Kim C M, Rim S, Kye W H, et al., Antisynchronization of chaotic oscillators, Phys. Lett. A, 2003, 320(1): 39–46.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Altafini C, Consensus problems on networks with antagonistic interactions, IEEE Trans. Automatic Control, 2013, 58(4): 935–946.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Hu J and Zheng W X, Emergent collective behaviors on coopetition networks, Phys. Lett. A, 2014, 378(26–27): 1787–1796.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Zhang H and Chen J, Bipartite consensus of general linear multi-agent systems, Proc. Amer. Control Conf., Portland, Oregon, USA, June 4–6, 2014.Google Scholar
  13. [13]
    Valcher M E and Misra P, On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions, Syst. Control Lett., 2014, 66(4): 94–103.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Proskurnikov A V, Matveev A, and Cao M, Opinion dynamics in social networks with hostile camps: Consensus vs. polarization, IEEE Trans. Automatic Control, 2016, 61(6): 1524–1536.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Huang M and Manton J H, Coordination and consensus of networked agents with noisy measurements: Stochastic algorithms and asymptotic behavior, SIAM J. Control Optim., 2009, 48(1): 134–161.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Li T and Zhang J F, Mean square average consensus under measurement noises and fixed topologies: Necessary and sufficient conditions, Automatica, 2009, 45(8): 1929–1936.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Ma C, Li T, and Zhang J F, Consensus control for leader-following multi-agent systems with measurement noises, Journal of Systems Science & Complexity, 2010, 23(1): 35–49.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Liu S, Xie L, and Zhang H, Distributed consensus for multiagent systems with delays and noises in transmission channels, Automatica, 2011, 47(5): 920–934.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    Gao L, Wang D, and Wang G, Further results on exponential stability for impulsive switched nonlinear time delay systems with delayed impulse effects, Applied Mathematics and Computation, 2015, 268: 186–200.MathSciNetCrossRefGoogle Scholar
  20. [20]
    Cheng L, Hou Z G, Tan M, et al., Necessary and sufficient conditions for consensus of doubleintegrator multi-agent systems with measurement noises, IEEE Trans. Automatic Control, 2011, 56(8): 1958–1963.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Cheng L, Wang Y P, Hou Z G, et al., Sampled-data based average consensus of second-order integral multi-agent systems: Switching topologies and communication noises, Automatica, 2013, 49(5): 1458–1464.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    Wang Y, Cheng L, Hou Z G, et al., Consensus seeking in a network of discrete-time linear agents with communication noises, Int. J. Syst. Science, 2015, 46(10): 1874–1888.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Ma C Q and Qin Z Y, Bipartite consensus on networks of agents with antagonistic interactions and measurement noises, IET Control Theory Appl., 2016, 10(17): 2306–2313.MathSciNetCrossRefGoogle Scholar
  24. [24]
    Ma C Q, Qin Z Y, and Zhao Y B, Bipartite consensus of integrator multi-agent systems with measurement noise, IET Control Theory Appl., 2017, 11(18): 3313–3320.MathSciNetCrossRefGoogle Scholar
  25. [25]
    Ma C Q, ZhaoW W, and Zhao Y B, Bipartite linear χ-consensus of double-integrator multi-agent systems with measurement noise, Asian Journal of Control, 2018, 20(2): 1–8.MathSciNetGoogle Scholar
  26. [26]
    Xie G M and Wang L, Consensus control for a class of networks of dynamic agents, Int. J. Robust Nonlin. Control, 2007, 17(10–11): 941–959.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    Meng D, Du M, and Jia Y, Interval bipartite consensus of networked agents associated with signed digraphs, IEEE Trans. Automatic Control, 2016, 61(12): 3755–3770.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    Cheng L, Wang Y, Hou Z G, et al., Convergence rate of leader-following consensus of networks of discrete-time linear agents in noisy environments, Proceedings of the 35th Chinese Control Conference, Chengdu, China, July 2016.CrossRefGoogle Scholar
  29. [29]
    Chow Y S and Teicher H, Probability Theory: Independence, Interchangeability, Martingales, 3rd Ed., Springer-Verlag, New York, 1997.CrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesQufu Normal UniversityQufuChina
  2. 2.No. 1 Senior Middle School of QufuQufuChina
  3. 3.College of Information EngineeringZhejiang University of TechnologyHangzhouChina

Personalised recommendations