Advertisement

Leader-following consensus of second-order nonlinear multi-agent systems subject to disturbances

  • Mao-Bin Lu
  • Lu LiuEmail author
Article

Abstract

In this study, we investigate the leader-following consensus problem of a class of heterogeneous secondorder nonlinear multi-agent systems subject to disturbances. In particular, the nonlinear systems contain uncertainties that can be linearly parameterized. We propose a class of novel distributed control laws, which depends on the relative state of the system and thus can be implemented even when no communication among agents exists. By Barbalat’s lemma, we demonstrate that consensus of the second-order nonlinear multi-agent system can be achieved by the proposed distributed control law. The effectiveness of the main result is verified by its application to consensus control of a group of Van der Pol oscillators.

Key words

Multi-agent systems Leader-following consensus Distributed control 

CLC number

TP182 

References

  1. Cheng L, Hou ZG, Tan M, et al., 2010. Neural-network-based adaptive leader-following control for multiagent systems with uncertainties. IEEE Trans Neur Netw, 21(8): 1351–1358. https://doi.org/10.1109/TNN.2010.2050601CrossRefGoogle Scholar
  2. Deng F, Guan S, Yue X, et al., 2017. Energy-based sound source localization with low power consumption in wireless sensor networks. IEEE Trans Ind Electron, 64(6): 4894–4902. https://doi.org/10.1109/TIE.2017.2652394CrossRefGoogle Scholar
  3. Godsil C, Royle G, 2001. Algebraic Graph Theory. Springer Berlin Heidelberg. https://doi.org/10.1007/978-1-4613-0163-9Google Scholar
  4. Hu JP, Hong YG, 2007. Leader-following coordination of multi-agent systems with coupling time delays. Phys A, 374(2):853–863. https://doi.org/10.1016/j.physa.2006.08.015CrossRefGoogle Scholar
  5. Jadbabaie A, Lin J, Morse AS, 2003. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Contr, 48(6):988–1001. https://doi.org/10.1109/TAC.2003.812781MathSciNetCrossRefzbMATHGoogle Scholar
  6. Liu W, Huang J, 2016. Leader-following consensus for uncertain second-order nonlinear multi-agent systems. Contr Theory Technol, 14(4):279–286. https://doi.org/10.1007/s11768-016-6082-xMathSciNetCrossRefzbMATHGoogle Scholar
  7. Lu MB, Liu L, 2017. Consensus of linear multi-agent systems subject to communication delays and switching networks. Int J Rob Nonl Contr, 27(9):1379–1396. https://doi.org/10.1002/rnc.3750MathSciNetzbMATHGoogle Scholar
  8. Lu MB, Liu L, 2018. Robust consensus of a class of heterogeneous nonlinear uncertain multi-agent systems subject to communication constraints. Chinese Control and Decision Conf, p.74–81. https://doi.org/10.1109/CCDC.2018.8407109Google Scholar
  9. Meng ZY, Lin ZL, Ren W, 2013. Robust cooperative tracking for multiple non-identical second-order nonlinear systems. Automatica, 49(8):2363–2372. https://doi.org/10.1016/j.automatica.2013.04.040MathSciNetCrossRefzbMATHGoogle Scholar
  10. Moreau L, 2004. Stability of continuous-time distributed consensus algorithms. Proc 43rd IEEE Conf on Decision and Control, p.3998–4003. https://doi.org/10.1109/CDC.2004.1429377Google Scholar
  11. Olfati-Saber R, 2006. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans Autom Contr, 51(3):401–420. https://doi.org/10.1109/TAC.2005.864190MathSciNetCrossRefzbMATHGoogle Scholar
  12. Olfati-Saber R, Murray RM, 2004. Consensus problems in networks of agents with switching topology and timedelays. IEEE Trans Autom Contr, 49(9):1520–1533. https://doi.org/10.1109/TAC.2004.834113CrossRefzbMATHGoogle Scholar
  13. Ren W, Beard RW, 2005. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Autom Contr, 50(5):655–661. https://doi.org/10.1109/TAC.2005.846556MathSciNetCrossRefzbMATHGoogle Scholar
  14. Slotine JJE, Li WP, 1991. Applied Nonlinear Control. Prentice-Hall.Google Scholar
  15. Song Q, Cao JD, Yu WW, 2010. Second-order leaderfollowing consensus of nonlinear multi-agent systems via pinning control. Syst Contr Lett, 59(9):553–562. https://doi.org/10.1016/j.sysconle.2010.06.016CrossRefzbMATHGoogle Scholar
  16. Su YF, 2015. Cooperative global output regulation of secondorder nonlinear multi-agent systems with unknown control direction. IEEE Trans Autom Contr, 60(12):3275–3280. https://doi.org/10.1109/TAC.2015.2426273CrossRefzbMATHGoogle Scholar
  17. Su YF, Huang J, 2012. Cooperative output regulation of linear multi-agent systems. IEEE Trans Autom Contr, 57(4):1062–1066. https://doi.org/10.1109/TAC.2011.2169618MathSciNetCrossRefzbMATHGoogle Scholar
  18. Su YF, Huang J, 2013. Cooperative global output regulation of heterogeneous second-order nonlinear uncertain multi-agent systems. Automatica, 49(11):3345–3350. https://doi.org/10.1016/j.automatica.2013.08.001MathSciNetCrossRefzbMATHGoogle Scholar
  19. Tuna SE, 2008. LQR-based coupling gain for synchronization of linear systems. https://arxiv.org/abs/0801.3390Google Scholar
  20. Wang CR, Ji HB, 2015. Robust consensus tracking for a class of heterogeneous second-order nonlinear multiagent systems. Int J Rob Nonl Contr, 25(17):3367–3383. https://doi.org/10.1002/rnc.3269CrossRefzbMATHGoogle Scholar
  21. Wieland P, Sepulchre R, Allgöwer F, 2011. An internal model principle is necessary and sufficient for linear output synchronization. Automatica, 47(5):1068–1074. https://doi.org/10.1016/j.automatica.2011.01.081MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of AutomationBeijing Institute of TechnologyBeijingChina
  2. 2.City University of Hong Kong Shenzhen Research InstituteShenzhenChina
  3. 3.Department of Biomedical EngineeringCity University of Hong KongHong KongChina

Personalised recommendations