Advertisement

Consensus of Second-order Multi-agent Systems with Directed Networks Using Relative Position Measurements Only

  • Shan ChengEmail author
  • Han Dong
  • Li Yu
  • Dongmei Zhang
  • Jinchen Ji
Regular Papers Control Theory and Applications
  • 87 Downloads

Abstract

This brief paper studies the consensus problem of second-order multi-agent systems when the agents’ velocity measurements are unavailable. Firstly, two simple consensus protocols which do not need velocity measurements of the agents are derived to guarantee that the multi-agent systems achieve consensus in directed networks. Secondly, a key constant which is determined by the complex eigenvalue of the nonsymmetric Laplacian matrix and an explicit expression of the consensus state are respectively developed based on matrix theory. The obtained results show that all the agents can reach consensus if the feedback parameter is bigger than the key constant. Thirdly, the theoretical analysis shows that the followers can track the position and velocity of the leader provided that the leader has a directed path to all other followers and the feedback parameter is bigger enough. Finally, numerical simulations are given to illustrate the effectiveness of the proposed protocols.

Keywords

Consensus directed networks multi-agent system velocity-free 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Jadbabaie, J. Lin, and A.S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Trans. on Automatic Control, vol. 48, no. 6, pp. 988–1001, June 2003.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    R. Olfati–Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and timedelays,” IEEE Trans. on Automatic Control, vol. 49, no. 9, pp. 1520–1533, September 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    W. Yu, G. Chen, and M. Cao, “Some necessary and sufficient conditions for second–order consensus in multi–agent dynamical systems,” Automatica, vol. 46, no. 6, pp. 1089–1095, June 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    J. Zhu, Y. Tian, and J. Kuang, “On the general consensus protocol of multi–agent systems with double–integrator dynamics,” Linear Algebra & Its Applications, vol. 431, no. 5–7, pp. 701–715, August 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Y. Liu, Y. Zhao, and G. Chen, “Finite–time formation tracking control for multiple vehicles: A motion planning approach,” International Journal of Robust&Nonlinear Control, vol. 26, no. 14, pp. 3130–3149, September 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Y. Zhao, Y. Liu, G. Wen, and G. Chen, “Distributed optimization for linear multi–agent systems: edge–and nodebased adaptive designs,” IEEE Trans. on Automatic Control, vol. 62, no. 7, pp. 3602–3609, February 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    L. Wu, Y. Gao, J. Liu, and H. Li “Event–triggered sliding mode control of stochastic systems via output feedback,” Automatica, vol. 82, pp. 79–92, August 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    L. Ding, Q. Han, X. Ge, and X. Zhang, “An overview of recent advances in event–triggered consensus of multiagent systems,” IEEE Trans. on Cybernetics, vol. 48, no. 4, pp. 1110–1123, April 2018.CrossRefGoogle Scholar
  9. [9]
    S. Cheng, J. Ji, and J. Zhou, “Second–order consensus of multiple non–identical agents with non–linear protocols,” IET Control Theory & Applications, vol. 6, no. 9, pp. 1319–1324, June 2012.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Y. Gao, L. Wang, and Y. Jia, “Consensus of multiple second–order agents without velocity measurements,” Proc. of the American Control Conference, St. Louis, MO, pp. 4464.4469, 2009.Google Scholar
  11. [11]
    A. Abdessameud and A. Tayebi, “On consensus algorithms for double–integrator dynamics without velocity measurements and with input constraints,” Systems & Control Letters, vol. 59, no. 12, pp. 812–821, December 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    C. Fan, Z. Chen, and H. Zhang, “Semi–global consensus of nonlinear second–order multi–agent systems with measurement output feedback,” IEEE Trans. on Automatic Control, vol. 59, no. 8, pp. 2222–2227, August 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    C. Ma, T. Li, and J. Zhang, “Consensus control for leaderfollowing multi–agent systems with measurements noises,” Journal of Systems Science & Complexity, vol. 23, no. 1, pp. 35–49, February 2010.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Q. Cui and J. Zhang, “On formability of linear continuoustime multi–agent systems,” Journal of Systems Science & Complexity, vol. 25, no. 1, pp. 13–29, February 2012.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Z. Wang, D. W. C. Ho, and X. Liu, “Variance–constrained filtering for uncertain stochastic systems with missing measurements,” IEEE Trans. on Automatic Control, vol. 48, no. 7, pp. 1254–1258, July 2003.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    W. Zhang and L. Yu, “Stabilization of sampled–data control systems with control inputs missing,” IEEE Trans. on Automatic Control, vol. 55, no. 2, pp. 447–452, February 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    D. Zhang, Z. Xu, H. Karimi, Q. Wang, and L. Yu, “Distributed H¥ output–feedback control for consensus of heterogeneous linear multi–agent systems with aperiodic sampled–data communications,” IEEE Trans. on Industrial Electronics, vol. 65, no. 5, pp. 4145–4155, May 2018.CrossRefGoogle Scholar
  18. [18]
    E. Nuño, L. Basañez, C. López–Franco, and N. Arana–Daniel, “Stability of nonlinear teleoperators using PD controllers without velocity measurements,” Journal of the Franklin Institute, vol. 351, pp. 241–256, January 2014.CrossRefzbMATHGoogle Scholar
  19. [19]
    C.I. Aldana, E. Nuño, L. Basañez, and E. Romero, “Operational space consensus of multiple heterogeneous robots without velocity measurements,” Journal of the Franklin Institute, vol. 351, no. 1, pp. 1517–1539, March 2014.CrossRefzbMATHGoogle Scholar
  20. [20]
    Y. Zheng and L. Wang, “Finite–time consensus of heterogeneous multi–agent systems with and without velocity measurements,” Systems & Control Letters, vol. 61, no. 8, pp. 871–878, August 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    H. Li, Y. Gao, L. Wu, and H. K. Lam, “Fault detection for T–S fuzzy time–delay systems: delta operator and inputoutput methods,” IEEE Trans. on Cybernetics, vol. 45, no. 2, pp. 229–241, February 2015.CrossRefGoogle Scholar
  22. [22]
    Z. Liu, Z. Guan, X. Shen, and G. Feng, “Consensus of multi–agent networks with aperiodic sampled communication via impulsive algorithms using position–only measurements,” IEEE Trans. on Automatic Control, vol. 57, no. 10, pp. 2639–2643, October 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    S. Djaidja and Q. Wu, “Leader–following consensus of single–integrator multi–agent systems under noisy and delayed communication,” International Journal of Control, Automation, and Systems, vol. 14, no. 2, pp. 357–366, April 2016.CrossRefGoogle Scholar
  24. [24]
    J. Mei, W. Ren, and G. Ma, “Distributed coordination for second–order multi–agent systems with nonlinear dynamics using only relative position measurements,” Automatica, vol. 49, no. 5, pp. 1419–1427, May 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    H. Liu, D. Li, Y. Yu, and Y. Zhong, “Robust trajectory tracking control of uncertain quadrotors without linear velocity measurements,” IET Control Theory & Applications, vol. 9, no. 11, pp. 1746–1754, July 2015.MathSciNetCrossRefGoogle Scholar
  26. [26]
    B. Zhang, Y. Jia, and F. Matsuno, “Finite–time observers for multi–agent systems without velocity measurements and with input saturations,” Systems & Control Letters, vol. 68, no. 1, pp. 86–94, June 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    Y. Zhao, Z. Duan, G. Wen, and G. Chen, “Distributed finite–time tracking of multiple non–identical second–order nonlinear systems with settling time estimation,” Automatica, vol. 64, pp. 86–93, February 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    X. Liu, M. Chen, H. Du, and S. Yang, “Further results on finite–time consensus of second–order multi–agent systems without velocity measurements,” International Journal of Robust & Nonlinear Control, vol. 26, no. 14, pp. 3170–3185, September 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    W. Zhang, Y. Liu, J. Lu, and J. Cao, “A novel consensus algorithm for second–order multi–agent systems without velocity measurements,” International Journal of Robust & Nonlinear Control, vol. 27, no. 15, pp. 2510–2528, October 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    C. Wen, F. Liu, Q. Song, and X. Feng, “Observer–based consensus of second–order multi–agent systems without velocity measurements,” Neurocomputing, vol. 179, pp. 298–306, February 2016.CrossRefGoogle Scholar
  31. [31]
    M. Homayounzade and M. Keshmiri, “Noncertainty equivalent adaptive control of robot manipulators without velocity measurements,” Advanced Robotics, vol. 28, no. 14, pp. 983–996, June 2014.CrossRefGoogle Scholar
  32. [32]
    D. Zhai and Y. Xia, “Robust saturation–based control of bilateral teleoperation without velocity measurements,” International Journal of Robust & Nonlinear Control, vol. 25, no. 15, pp. 2582–2607, October 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    Q. Hu and J. Zhang, “Relative position finite–time coordinated tracking control of spacecraft formation without velocity measurements,” ISA Trans., vol. 54, pp. 60–74, January 2015.CrossRefGoogle Scholar
  34. [34]
    L. Ding, W. Zheng, and G. Guo, “Network–based practical set consensus of multi–agent systems subject to input saturation,” Automatica, vol. 89, no. 3, pp. 316–324, March 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    Y. Zhao, Z. Duan, and G. Wen, “Distributed finite–time tracking of multiple Euler–Lagrange systems without velocity measurements,” International Journal of Robust & Nonlinear Control, vol. 25, no. 11, pp. 1688–1703, July 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    J. TaheriKalani and N. Zarei, “An adaptive technique for trajectory tracking control of a wheeled mobile robots without velocity measurements,” Automatic Control & Computer Sciences, vol. 50, no. 6, pp. 441–452, November 2016.CrossRefGoogle Scholar
  37. [37]
    H. Min, S. Wang, F. Sun, and J. Zhang, “Robust consensus for networked mechanical systems with coupling time delay,” International Journal of Control, Automation, and Systems, vol. 10, no. 2, pp. 227–237, April 2012.CrossRefGoogle Scholar
  38. [38]
    X. Liang, H. Wang, Y. Liu, and W. Chen, “Adaptive taskspace cooperative tracking control of networked robotic manipulators without task–space velocity measurements,” IEEE Trans. on Cybernetics, vol. 46, no. 10, pp. 2386–2398, October 2016.CrossRefGoogle Scholar
  39. [39]
    S. Cheng, L. Yu, D. Zhang, L. Huo, and J. Ji, “Consensus of second–order multi–agent systems using partial agents’ velocity measurements,” Nonlinear Dyn., vol. 86, no. 3, pp. 1927–1935, November 2016.CrossRefzbMATHGoogle Scholar
  40. [40]
    W. Ren, “Synchronization of coupled harmonic oscillators with local interaction,” Automatica, vol. 44, no. 44, pp. 3195–3200, December 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    M. Marden, Geometry of Polynomials, American Mathematical Society, New Jersey, 1970.Google Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Shan Cheng
    • 1
    Email author
  • Han Dong
    • 2
  • Li Yu
    • 1
  • Dongmei Zhang
    • 2
  • Jinchen Ji
    • 3
  1. 1.College of Information EngineeringZhejiang University of TechnologyHangzhouChina
  2. 2.College of ScienceZhejiang University of TechnologyHangzhouChina
  3. 3.Faculty of Engineering and ITUniversity of TechnologyBroadwayAustralia

Personalised recommendations