Skip to main content
Log in

Iterative Consensus for a Class of Second-order Multi-agent Systems

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

In this paper, the problem of leader-following consensus for a class of multi-agent systems with double integrator dynamics is investigated based on an iterative learning approach. Consensus errors of individual agents are considered as the anticipation in time, based on which a distributed iterative learning protocol is proposed for the undirected networks with fixed topology to make the followers track the leader in finite time. The dynamic of the leader is assumed to be time-varying and the state information is available to only a portion of the followers. The sufficient condition for solving the consensus problem of the multi-agent system is obtained. A simulation example is provided to demonstrate the effectiveness of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Fax, A., Murray, R.: Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control 49(9), 1465–1476 (2004)

    Article  MathSciNet  Google Scholar 

  2. Moreau, L.: Stability of multiagent systems with time-dependent communication links. IEEE Trans. Autom. Control 50(2), 169–182 (2005)

    Article  MathSciNet  Google Scholar 

  3. Zavlanos, M.A., Pappas, G.J.: Distributed connectivity control of mobile networks. IEEE Trans. Robot. 24(6), 1416–1428 (2008)

    Article  Google Scholar 

  4. Zambonelli, F., Jennings, N.R., Wooldridge, M.: Developing multiagent systems: the Gaia methodology. ACM Trans. Softw. Eng. Methodol. 12(3), 317–370 (2003)

    Article  Google Scholar 

  5. Wachowiak, M.P., Smolikova, R., Zheng, Y.F.: An approach to multimodal biomedical image registration utilizing particle swarm optimization. IEEE Trans Evol. Comput. 8(3), 289–301 (2004)

    Article  Google Scholar 

  6. Fan, X., Chen, P., Yen, J.: An approach to multimodal biomedical image registration utilizing particle swarm optimization. Cogn. Syst. Res. 11(1), 108–119 (2010)

    Article  Google Scholar 

  7. Zhu, S., Wang, D., Low, C.: Cooperative control of multiple UAVs for source seeking. J. Intell. Robot. Syst. 70(1), 293–301 (2013)

    Article  Google Scholar 

  8. Guo, H., Yan, M.: Distributed reinforcement learning for coordinate multi-robot foraging. J. Intell. Robot. Systs. 60(3), 531–551 (2010)

    Article  MATH  Google Scholar 

  9. Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control 51(3), 401–420 (2006)

    Article  MathSciNet  Google Scholar 

  10. Qi, H., Iyengar, S., Chakrabarty, K.: Multi resolution data integration using mobile agents in distributed sensor networks. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 31(3), 383–391 (2001)

    Article  Google Scholar 

  11. Hwang, H., Tan, S., Hsiao, H.: Cooperative multi-agent congestion control for high-speed networks. IEEE Trans. Syst. Man Cybern. Part B Cybern. 35(2), 255–268 (2005)

    Article  Google Scholar 

  12. Olfati-Saber, R.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)

    Article  MathSciNet  Google Scholar 

  13. Ren, W., Beard, R.W.: Consensus seeking in multi-agent systems using dynamically changing interaction topologies. IEEE Trans. Autom. Control 50(5), 655–661 (2005)

    Article  MathSciNet  Google Scholar 

  14. Olfati-Saber, R., Fax, J., Murray, R.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 1–17 (2007)

    Article  Google Scholar 

  15. Hong, H., Hu, J., Gao, L.: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42(7), 1177–1182 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Yu, W., Zheng, W., Chen, G., Ren, W., Cao, J.: Second-order consensus in multi-agent dynamical systems with sampled position data. Automatica 47(7), 1496–1503 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  17. He, W., Cao, J.: Consensus control for high-order multi-agent systems. IET Control Theory Appl. 5(1), 231–238 (2011)

    Article  MathSciNet  Google Scholar 

  18. Bristow, D.A., Tharayil, M., Alleyne, A.G.: A survey of iterative learning control. IEEE Control Syst. Mag. 26(3), 69–114 (2006)

    Article  Google Scholar 

  19. Xu, J., Zhang, S., Yang, S.: A HOIM-based iterative learning control scheme for multi-agent formation. In: Proceedings of the IEEE Conference on International Symposium on Intelligent Control, pp. 418–423 (2011)

  20. Hyo-Sung, A., Chen, Y.: Iterative learning control for multi-agent formation. In: Proceedings of the ICROS-SICE International Joint Conference, pp. 3111–3116 (2009)

  21. Schöllig, A., Alonso-Mora, J., Raffaello D.A.: Independent vs. joint estimation in multi-agent iterative learning control. In: Proceedings of the IEEE Conference on Decision and Control, pp. 6949–6954 (2010)

  22. Hyo-Sung, A., Chen, Y., Moore, K.L.: Multi-agent coordination by iterative learning control: centralized and decentralized strategies. In: Proceedings of the IEEE Conference on Systems and Control, pp. 394–399 (2011)

  23. Meng, D., Jia, Y.: Finite-time consensus for multi-agent systems via terminal feedback iterative learning. IET Control Theory Appl. 5(18), 2098–2110 (2011)

    Article  MathSciNet  Google Scholar 

  24. Meng, D., Jia, Y.: Iterative learning approaches to design finite time consensus protocols for multi-agent systems. Syst. Control Lett. 61(1), 187–194 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  25. Liu, Y., Jia, Y.: Formation control of discrete-time multi-agent systems by iterative learning approach. Int. J. Control Autom. Syst. 10(5), 913–919 (2012)

    Article  Google Scholar 

  26. Meng, D., Jia, Y.: Formation control for multi-agent systems through an iterative learning design approach. Int. J. Robust Nonlinear Control (2012). doi:10.1002/rnc.2890

    Google Scholar 

  27. Liu, Y., Jia, Y.: An iterative learning approach to formation control of multi-agent systems. Syst. Control Lett. 61(1), 148–154 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  28. Yang, S., Xu, J.: Adaptive iterative learning control for multi-agent systems consensus tracking. In: Proceedings of the IEEE Conference on Systems, Man and Cybernetics, pp. 14–17 (2012)

  29. Ren, W.: On consensus algorithms for double-integrator dynamics. IEEE Trans. Autom. Control 53(6), 1503–1509 (2008)

    Article  Google Scholar 

  30. Horn, A., Johnson, R.: Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Donghua Zhou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shi, J., He, X., Wang, Z. et al. Iterative Consensus for a Class of Second-order Multi-agent Systems. J Intell Robot Syst 73, 655–664 (2014). https://doi.org/10.1007/s10846-013-9996-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-013-9996-2

Keywords

Navigation