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Leader-following consensus of double-integrator multi-agent systems with noisy measurements

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Abstract

This paper proposes a leader-following consensus control for continuous-time double-integrator multi-agent systems in noisy communication environment with a constant velocity reference state. Each follower in the team inaccurately measures its neighbors’ positions and the leader’s position if this follower has access to the leader, that the measured positions are corrupted by noises. The constant velocity of the leader is a priori well known. The consensus protocol is constructed based on algebraic graph theory and some stochastic tools. Conditions to ensure the tracking consensus in mean square are derived for both fixed and switching directed topologies. Finally, to illustrate the approach presented, some numerical simulations are carried out.

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References

  1. W. Ren and R. W. Beard, Distributed Consensus in Multi-vehicle Cooperative Control, Ser. Communications and Control Engineering, Springer-Verlag, London, 2008.

    Google Scholar 

  2. K. Liu, G. M. Xie, W. Ren, and L. Wang, “Consensus for multi-agent systems with inherent nonlinear dynamics under directed topologies,” Systems & Control Letters, vol. 62, no. 2, pp. 152–162, 2013.

    Article  MATH  MathSciNet  Google Scholar 

  3. Y. Cao and W. Ren, “Finite-time consensus for second-order multi-agent networks with inherent nonlinear dynamics under an undirected fixed graph,” Proc. of the 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA, December 12–15, 2011.

    Google Scholar 

  4. A. Abdessameud and A. Tayebi, “On consensus algorithms for double integrator dynamics without velocity measurements and with input constraints,” Systems and Control Letters, vol. 59, no. 12, pp. 812–821, 2010.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Hu and Y. S. Lin, “Consensus control for multi-agent systems with double-integrator dynamics and time delays,” IET Control Theory and Applications, vol. 4, no. 1, pp. 109–118, 2010.

    Article  MathSciNet  Google Scholar 

  6. W. Ren, R. W. Beard, and D. B. Kingston, “Multiagent Kalman consensus with relative uncertainty,” Proc. of the American Control Conference, pp. 1865–1870, 2005.

    Google Scholar 

  7. M. Huang and J. H. Manton, “Coordination and consensus of networked agents with noisy measurement: stochastic algorithms and asymptotic behavior,” SIAM Journal on Control and Optimization, vol. 48, no. 1, pp. 134–161, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Huang and J. H. Manton, “Stochastic approximation for consensus seeking: mean square and almost sure convergence,” Proc. of the 46th IEEE Conference on Decision and Control, pp. 306–311, New Orleans, LA, USA, December 2007.

    Google Scholar 

  9. M. Huang and J. H. Manton, “Stochastic consensus seeking with measurement noise: convergence and asymptotic normality,” Proc. of the American Control Conference, pp. 1337–1342, Seattle, WA, USA, June 2008.

    Google Scholar 

  10. T. Li and J. F. Zhang, “Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises,” IEEE Trans. on Automatic Control, vol. 55, no. 9, pp. 2043–2057, 2010.

    Article  Google Scholar 

  11. T. Li and J. F. Zhang, “Mean square averageconsensus under measurement noises and fixed topologies: necessary and sufficient conditions,” Automatica, vol. 45, no. 8, pp. 1929–1936, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  12. J. Liu, X. Z. Liu, W. C. Xie, and H. T. Zhang, “Stochastic consensus seeking with communication delays,” Automatica, vol. 47, no. 12, pp. 2689–2696, 2011.

    Article  MATH  MathSciNet  Google Scholar 

  13. J. P. Hu and G. Feng, “Distributed tracking control of leader-follower multi-agent systems under noisy measurement,” Automatica, vol. 46, no. 8, pp. 1382–1387, 2010.

    Article  MATH  MathSciNet  Google Scholar 

  14. Y. L. Shang, “Leader-following consensus problems with a time-varying leader under measurement noises,” Advances in Dynamical Systems and Applications, vol. 6, no. 2, pp. 255–270, 2011.

    MathSciNet  Google Scholar 

  15. C. Q. Ma, T. Li, and J. F. Zhang, “consensus control for leader-following multi-agent systems with measurement noises,” Journal of Systems Science and Complexity, vol. 23, no. 1, pp. 35–49, 2010.

    Article  MATH  MathSciNet  Google Scholar 

  16. W. H. Ni and X. Li, “Consensus seeking in multiagent systems with multiplicative measurement noises,” Systems & Control Letters, vol. 62, no. 5, pp. 430–437, 2013.

    Article  MATH  MathSciNet  Google Scholar 

  17. T. Li, F. Wu, and J. F. Zhang, “Consensus conditions of continuous-time multi-agent systems with relative-state-dependent measurement noises and matrix-valued intensity functions,” Proc. of the 9th Asian Control Conference, Istanbul, Turkey, 2013.

    Google Scholar 

  18. S. Djaidja and Q. H. Wu, “Leader-following consensus for single-integrator multi-agent systems with multiplicative noises in directed topologies,” International Journal of Systems Science, DOI: 10.1080/00207721.2013.879233, 2014.

    Google Scholar 

  19. X. L. Liu, B. G. Xu, and L. H. Xie, “Mean square consensus control for second order multi-agent systems under fixed topologies and measurement noises,” Advanced Materials Research, vol. 403–408, pp. 4036–4043, 2011.

    Article  Google Scholar 

  20. L. Cheng, Z. G. Hou, M. Tan, and X. Wang, “Necessary and sufficient conditions for consensus of double-integrator multi-agent systems with measurement noises,” IEEE Trans. on Automatic Control, vol. 56, no. 8, pp. 1958–1963, 2011.

    Article  MathSciNet  Google Scholar 

  21. X. Q. Liu and S. H. Cheng, “Tracking consensus for second-order multi-agent systems with nonlinear dynamics in noisy environments,” Communication in Theoretical Physics, vol. 59, no. 4, pp. 429–438, 2013.

    Article  MathSciNet  Google Scholar 

  22. Z. H. Wu, L. Peng, L. B. Xie, and J. W. Wen, “Stochastic bounded consensus tracking of second-order multi-agent systems with measurement noises based on sampled-data with small sampling delay,” International Journal of Control, Automation, and Systems, vol. 12, no. 1, pp. 44–56, 2014.

    Article  Google Scholar 

  23. W. Ren, “Consensus seeking in multi-vehicle systems with a time-varying reference state,” Proc. of the American Control Conference, pp. 717–722, New York, July 2007.

    Google Scholar 

  24. J. Hu and Y. Hong, “Leader-following coordination of multi-agent systems with coupling time delays,” Physica A, vol. 374, no. 2, pp. 853–863, 2007.

    Article  Google Scholar 

  25. B. Øksendal, Stochastic Differential Equations, An Introduction with Applications, 6th edition, New York, Springer, 2003.

    Google Scholar 

  26. A. N. Michel and R. K. Miller, Qualitative Analysis of Large Scale Dynamical Systems, Academic, Press, New York, 1977.

    MATH  Google Scholar 

Download references

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Correspondence to Sabir Djaidja.

Additional information

Sabir Djaidja was born in 1985. He received his B.Eng. degree in Control Systems from ENPEI and EMP, Algiers, Algeria in 2009. He is currently a Ph.D. student with the School of Automation in Beijing Institute of Technology, Beijing, China. His research interests include control of multi-agent systems, stochastic systems, optimal cooperative control, etc.

Qing He Wu received his B.Eng. degree in Electrical Engineering from Huazhong University of Science and Technology, Wuhan, China in 1982, the post-graduate diploma and the Dr. Tech. Sci. degrees from the Swiss Federal Institute of Technology (ETHZ), Zurich, Switzerland, in 1984 and 1990 respectively. From 1986 to 1994 he has been Assistent and Oberassistent with the Institute of Automatic Control, ETHZ. Since 1995, he has been with the Beijing Institute of Technology, Beijing, China, where he has been Professor since 1997. He was a Visiting Research Fellow from July 2002 to June 2003 in Akita Prefectural University, Akita, Japan. His research interests include H-infinity control and robust control theory.

Hao Fang received his B.S. degree from the Xi’an University of Technology, Xi’an, China in 1995, and his M.S. and Ph.D. degrees from the Xi’an Jiaotong University, Xi’an, China, in 1998 and 2002, respectively. He held two Postdoctoral appointments at the INRIA/France Research Group of COPRIN and at the LASMEA, UNR6602 CNRS/Blaise Pascal University, Clermont-Ferrand, France. Since 2011, he has been a Professor with the Beijing Institute of Technology, Beijing, China. His research interests include multi-agent system, robotic control.

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Djaidja, S., Wu, Q.H. & Fang, H. Leader-following consensus of double-integrator multi-agent systems with noisy measurements. Int. J. Control Autom. Syst. 13, 17–24 (2015). https://doi.org/10.1007/s12555-013-0511-0

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  • DOI: https://doi.org/10.1007/s12555-013-0511-0

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