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Reaching a stochastic consensus in the noisy networks of linear MIMO agents: Dynamic output-feedback and convergence rate

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Abstract

This paper addresses the leader-following consensus problem of linear multi-agent systems (MASs) with communication noise. Each agent’s dynamical behavior is described by a linear multi-input and multi-output (MIMO) system, and the agent’s full state is assumed to be unavailable. To deal with this challenge, a state observer is constructed to estimate the agent’s full state. A dynamic output-feedback based protocol that is based on the estimated state is proposed. To mitigate the effect of communication noise, noise-attenuation gains are also introduced into the proposed protocol. In this study, each agent is allowed to have its own noise-attenuation gain. It is shown that the proposed protocol can solve the mean square leader-following consensus problem of a linear MIMO MAS. Moreover, if all noise-attenuation gains are of Θ(t -β), where β∈(0,1), the convergence rate of the MAS can be quantitatively analyzed. It turns out that all followers’ states converge to the leader’s state in the mean square sense at a rate of O(t -β).

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References

  1. Ren W, Beard R W, Atkins E M. A survey of consensus problems in multi-agent coordination. In: Proceedings of 2005 American Control Conference, Portland, 2005. 1859–1864

    Google Scholar 

  2. Olfati-Saber R, Fax J A, Murray R M. Consensus and cooperation in networked multi-agent systems. Proc IEEE, 2007, 95: 215–233

    Article  Google Scholar 

  3. Huang M, Manton J H. Coordination and consensus of networked agents with noisy measurements: Stochastic algorithms and asymptotic behavior. SIAM J Control Optim, 2009, 48: 134–161

    Article  MathSciNet  MATH  Google Scholar 

  4. Kar S, Moura J M F. Distributed consensus algorithms in sensor networks: Link failures and channel noise. IEEE T Signal Process, 2009, 57: 355–369

    Article  Google Scholar 

  5. Li T, Zhang J-F. Mean square average-consensus under measurement noises and fixed topologies: Necessary and sufficient conditions. Automatica, 2009, 45: 1929–1936

    Article  MATH  Google Scholar 

  6. Huang M, Manton J H. Stochastic consensus seeking with noisy and directed inter-agent communication: Fixed and randomly varying topologies. IEEE T Automat Contr, 2010, 55: 235–241

    Article  MathSciNet  Google Scholar 

  7. Li T, Zhang J F. Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises. IEEE T Automat Contr, 2010, 55: 2043–2057

    Article  Google Scholar 

  8. Zhang Q, Zhang J F. Distributed parameter estimation over unreliable networks with Markovian switching topologies. IEEE T Automat Contr, 2012, 57: 2545–2560

    Article  Google Scholar 

  9. Cheng L, Hou Z G, Tan M, et al. Necessary and sufficient conditions for consensus of double-integrator multi-agent systems with measurement noises. IEEE T Automat Contr, 2011, 56: 1958–1963

    Article  MathSciNet  Google Scholar 

  10. Cheng L, Wang Y, 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: 1458–1464

    Article  MathSciNet  Google Scholar 

  11. Cheng L, Hou Z G, Tan M. A mean square consensus protocol for linear multi-agent systems with communication noises and fixed topologies. IEEE T Automat Contr, 2014, 59: 261–267

    Article  MathSciNet  Google Scholar 

  12. 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 Sci, 2015, 46: 1874–1888

    Article  MathSciNet  Google Scholar 

  13. Wang Y, Cheng L, Ren W, et al. Seeking consensus in networks of linear agents: Communication noises and Markovian switching. IEEE T Automat Contr, 2015, 60: 1374–1379

    Article  MathSciNet  Google Scholar 

  14. Ma C-Q, Zhang J-F. Consensus control for leader-following multi- agent systems with measurement noises. J Syst Sci Complexity, 2010, 23: 35–49

    Article  MATH  Google Scholar 

  15. Hu J, Feng G. Distributed tracking control of leader-following multi- agent systems under noisy measurement. Automatica, 2010, 46: 1382–1387

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang Y, Cheng L, Hou Z G, et al. Containment control of multi- agent systems in a noisy communication environment. Automatica, 2014, 50: 1922–1928

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang Y, Cheng L, Hou Z G, et al. Leader-following output consensus in a network of linear agents with communication noises. In: Proceedings of 2014 IFAC World Congress. Cape Town, 2014. 1825–1830

    Google Scholar 

  18. Tang H, Li T. On asymptotic properties of continuous-time stochastic approximation type consensus protocols. In: Proceedings of the 53rd IEEE Conference on Decision and Control. Los Angeles: IEEE, 2014. 2210–2215

    Chapter  Google Scholar 

  19. Tang H, Li T. Continuous-time stochastic consensus: Stochastic approximation and Kalman-Bucy filtering based protocols. Automatica, 2015, 61: 146–155

    Article  Google Scholar 

  20. Cheng L, Wang Y, Ren W, et al. On convergence rate of leader- following consensus of linear multi-agent systems with communication noises. IEEE T Automat Contr, 2015, doi: 1508.06927

    Google Scholar 

  21. Meng Z, Ren W, You Z. Distributed finite-time attitude containment control for multiple rigid bodies. Automatica, 2010, 46: 2092–2099.

    Article  MathSciNet  MATH  Google Scholar 

  22. Yokoyama R, Kinnen E. Phase-variable canonical forms for linear, multi-input, multi-output systems. Int J Control, 1973, 17: 1297–1312

    Article  MathSciNet  MATH  Google Scholar 

  23. Cheng L, Hou Z G, Lin Y, et al. Solving a modified consensus problem of linear multi-agent systems. Automatica, 2011, 47: 2218–2223.

    Article  MathSciNet  MATH  Google Scholar 

  24. Cheng L, Wang H, Hou Z G, et al. Reaching a consensus in networks of high-order integral agents under switching directed topologies. Int J Syst Sci, 2015, doi: 10.1080/00207721.2014.966281

    Google Scholar 

  25. Canuto C, Tabacco A. Mathematical Analysis I. Milan: Springer-Verlag, 2008

    Book  Google Scholar 

  26. Zhou J, Wu X, Liu Z, Distributed coordinated adaptive tracking in networked redundant robotic systems with a dynamic leader. Sci China Tech Sci, 2014, 57: 905–913

  27. Wang X, Zhu J, Yang J, et al. Coordination control strategy based on characteristic model for 3-bearing swivel duct nozzles. Sci China Tech Sci, 2014, 57: 2347–2356

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China

    YunPeng Wang, Long Cheng, ZengGuang Hou & Min Tan

  2. Plymouth University, Plymouth, PL48AB, UK

    ChenGuang Yang

  3. College of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, China

    ChenGuang Yang

Authors
  1. YunPeng Wang
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  2. Long Cheng
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  3. ChenGuang Yang
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  4. ZengGuang Hou
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  5. Min Tan
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Correspondence to Long Cheng.

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Wang, Y., Cheng, L., Yang, C. et al. Reaching a stochastic consensus in the noisy networks of linear MIMO agents: Dynamic output-feedback and convergence rate. Sci. China Technol. Sci. 59, 45–54 (2016). https://doi.org/10.1007/s11431-015-5975-0

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  • DOI: https://doi.org/10.1007/s11431-015-5975-0

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