Continuous-time multi-agent averaging with relative-state-dependent measurement noises: matrix intensity functions

Tao Li; Fuke Wu; Ji-Feng Zhang

Continuous-time multi-agent averaging with relative-state-dependent measurement noises: matrix intensity functions

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Author(s): Tao Li ¹ ; Fuke Wu ² ; Ji-Feng Zhang ³
- Affiliations: 1: School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, People's Republic of China;
  2: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China;
  3: Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
Source: Volume 9, Issue 3, 05 February 2015, p. 374 – 380
DOI: 10.1049/iet-cta.2014.0467 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 28/04/2014, Accepted 29/08/2014, Revised 10/07/2014, Published 22/01/2015

In this study, the distributed averaging of high-dimensional first-order agents is investigated with relative-state-dependent measurement noises. Each agent can measure or receive its neighbours’ state information with random noises, whose intensity is a non-linear matrix function of agents’ relative states. By the tools of stochastic differential equations and algebraic graph theory, the authors give sufficient conditions to ensure mean square and almost sure average consensus and the convergence rate and the steady-state error for average consensus are quantified. Especially, if the noise intensity function depends linearly on the relative distance of agents’ states, then a sufficient condition is given in terms of the control gain, the noise intensity coefficient constant, the number of agents and the dimension of agents’ dynamics.

References

1. 1)
  - P. Frasca , R. Carli , F. Fagnani , S. Zampieri . Average consensus on networks with quantized communication. Int. J. Robust Nonlinear Control , 10 , 1787 - 1816
2. 2)
  - 6. Wang, J., Elia, N.: ‘Distributed averaging under constraints on information exchange: emergence of Levy flights’, IEEE Trans. Autom. Control, 2012, 57, (10), pp. 2435–2449 (doi: 10.1109/TAC.2012.2186093).
3. 3)
  - 24. Mao, X.: ‘Stochatic differential equations and applications’ (Horwood Publishing, Chichester, England, 1997).
4. 4)
  - 2. Kar, S., Moura, J.M.F.: ‘Distributed consensus algorithms in sensor networks with imperfect communication: link failures and channel noise’, IEEE Trans. Signal Process., 2009, 57, (1), pp. 355–369 (doi: 10.1109/TSP.2008.2007111).
5. 5)
  - M. Huang , J.H. Manton . Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior. SIAM J. Control Optim. , 1 , 134 - 161
6. 6)
  - 17. Cheng, L., Hou, Z.G., Tan, M.: ‘A mean square consensus protocol for linear multi-agent systems with communication noises and fixed topologies’, IEEE Trans. Autom. Control, 2014, 59, (1), pp. 261–267 (doi: 10.1109/TAC.2013.2270873).
7. 7)
  - N. Elia . Remote stabilisation over fading channels. Syst. Control Lett. , 3 , 237 - 249
8. 8)
  - J. Liu , X.Z. Liu , W.H. Xie , H.T. Zhang . Stochastic consensus seeking with communication delays. Automatica , 12 , 2689 - 2696
9. 9)
  - 16. Cheng, L., Hou, Z.G., Tan, M., Wang, X.: ‘Necessary and sufficient conditions for consensus of double-integrator multi-agent systems with measurement noises’, IEEE Trans. Autom. Control, 2011, 56, (8), pp. 1958–1963 (doi: 10.1109/TAC.2011.2139450).
10. 10)
  - R. Olfati-Saber , R.M. Murray . Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control , 9 , 1520 - 1533
11. 11)
  - 5. Huang, M., Manton, J.H.: ‘Stochastic consensus seeking with noisy and directed inter-agent communication: fixed and randomly varying topologies’, IEEE Trans. Autom. Control, 2010, 55, (1), pp. 235–241 (doi: 10.1109/TAC.2009.2036291).
12. 12)
  - R. Carli , F. Bullo . Quantized coordination algorithms for rendezvous and deployment. SIAM J. Control Optim. , 3 , 1251 - 1274
13. 13)
  - 19. Li, T., Wu, F.K., Zhang, J.F.: ‘Multi-agent consensus with relative-state-dependent measurement noises’, IEEE Trans. Autom. Control, 2014, 59, (9), pp. 2463–2468 (doi: 10.1109/TAC.2014.2304368).
14. 14)
  - A. Kashyap , T. Basar , R. Srikant . Quantized consensus. Automatica , 6 , 1192 - 1203
15. 15)
  - 15. Ma, C.Q., Li, T., Zhang, J.F.: ‘Consensus control for leader-following multi-agent systems with measurement noises’, J. Syst. Sci. Complexity, 2010, 23, (1), pp. 35–49 (doi: 10.1007/s11424-010-9273-4).
16. 16)
  - 23. Michel, A.N., Miller, R.K.: ‘Qualitative analysis of large scale dynamical systems’ (Academic Press, New York, USA, 1977).
17. 17)
  - T. Li , J. Zhang . Mean square average-consensus under measurement noises and fixed topologies: necessary and sufficient conditions. Automatica , 1929 - 1936
18. 18)
  - 20. Bolognani, S., Favero, S.D., Schenato, L., Varagnolo, D.: ‘Consensus-based distributed sensor calibration and least-square parameter identification in WSNs’, Int. J. Robust Nonlinear Control, 2010, 20, (2), pp. 176–193 (doi: 10.1002/rnc.1452).
19. 19)
  - 9. Lavaei, J., Murray, R.M.: ‘Quantized consensus by means of gossip algorithm’, IEEE Trans. Autom. Control, 2012, 57, (1), pp. 19–32 (doi: 10.1109/TAC.2011.2160593).
20. 20)
  - T. Li , J.F. Zhang . Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises. IEEE Trans. Autom. Control , 9 , 2043 - 2057
21. 21)
  - 13. Li, T., Xie, L.: ‘Distributed consensus over digital networks with limited bandwidth and time-varying topologies’, Automatica, 2011, 47, (9), pp. 2006–2015 (doi: 10.1016/j.automatica.2011.05.017).
22. 22)
  - T. Li , M. Fu , L. Xie , J. Zhang . Distributed consensus with limited communication date rate. IEEE Trans. Autom. Control , 2 , 279 - 291
23. 23)
  - R. Carli , F. Fagnani , A. Speranzon , S. Zampieri . Communication constraints in the average consensus problem. Automatica , 3 , 671 - 684
24. 24)
  - 4. Schenato, L., Fiorentin, F.: ‘Average TimeSynch: a consensus-based protocol for clock synchronization in wireless sensor networks’, Automatica, 2011, 47, (9), pp. 1878–1886 (doi: 10.1016/j.automatica.2011.06.012).

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Continuous-time multi-agent averaging with relative-state-dependent measurement noises: matrix intensity functions

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