Kybernetika 51 no. 2, 335-346, 2015

Output consensus of nonlinear multi-agent systems with unknown control directions

Yutao TangDOI: 10.14736/kyb-2015-2-0335

Abstract:

In this paper, we consider an output consensus problem for a general class of nonlinear multi-agent systems without a prior knowledge of the agents' control directions. Two distributed Nussbaum-type control laws are proposed to solve the leaderless and leader-following adaptive consensus for heterogeneous multiple agents. Examples and simulations are given to verify their effectiveness.

Keywords:

adaptive control, output consensus, heterogeneous multi-agent system, unknown control direction

Classification:

93A14, 93C40

paper.pdf

References:

  1. H. Bai, M. Arcak and J. Wen: Cooperative Control Design: A Systematic, Passivity-Based Approach Springer-Verlag, New York 2011.   CrossRef
  2. W. Chen, X. Li, W. Ren and C. Wen: Adaptive consensus of multi-agent systems with unknown identical control directions based on a novel Nussbaum-type function. IEEE Trans. Automat. Control 59 (2014), 1887-1892.   DOI:10.1109/tac.2013.2293452
  3. N. Chopra and M. W. Spong: Passivity-based control of multi-agent systems. In: Advances in Robot Control (S. Kawamura and M. Svinin, eds.), Springer Verlag, Berlin 2006, pp. 107-134.   DOI:10.1007/978-3-540-37347-6_6
  4. J. Du, C. Guo, S. Yu and Y. Zhao: Adaptive autopilot design of time-varying uncertain ships with completely unknown control coefficient. IEEE J. Ocean. Eng. 32 (2007), 346-352.   DOI:10.1109/joe.2007.893684
  5. L. Gao, Y. Tang, W. Chen and H. Zhang: Consensus seeking in multi-agent systems with an active leader and communication delays. Kybernetika 47 (2011), 773-789.   CrossRef
  6. A. Hamadeh, G. Stan, R. Sepulchre and J. Gonçalves: Global state synchronization in networks of cyclic feedback systems. IEEE Trans. Automat. Control 57(2012), 478-483.   DOI:10.1109/tac.2011.2164015
  7. Y. Hong, J. Hu and L. Gao: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42 (2006), 1177-1182.   DOI:10.1016/j.automatica.2006.02.013
  8. Y. Hong and X. Wang: Multi-agent tracking of a high-dimensional active leader with switching topology. J. Syst. Sci. Complex. 22 (2009), 722-731.   DOI:10.1007/s11424-009-9197-z
  9. J. Hu and Y. Hong: Leader-following coordination of multi-agent systems with coupling time delays. Phys. A 374 (2007), 853-863.   DOI:10.1016/j.physa.2006.08.015
  10. B. Jayawardhana: Tracking and disturbance rejection for passive nonlinear systems. In: Proc. 44th IEEE Conference on Decision and Control and 2005 European Control Conference. Chicago 2005, pp. 3333-3338.   DOI:10.1109/cdc.2005.1582676
  11. H. K. Khalil: Nonlinear Systems. Third edition. Prentice Hall, New Jersey 2002.   CrossRef
  12. Y. Liu and G. Tao: Multivariable MRAC using Nussbaum gains for aircraft with abrupt damages. In: Proc. 47th IEEE Conference on Decision and Control. Cancun 2008, pp. 2600-2605.   DOI:10.1109/cdc.2008.4739463
  13. M. Mesbahi and M. Egerstedt: Graph Theoretic Methods in Multiagent Networks. Princeton University Press, New Jersey 2010.   CrossRef
  14. W. Ni and D. Cheng: Leader-following consensus of multi-agent systems under fixed and switching topologies. Systems Control Lett. 59 (2010), 209-217.   DOI:10.1016/j.sysconle.2010.01.006
  15. R. D. Nussbaum: Some remarks on a conjecture in parameter adaptive control. Systems Control Lett. 3 (1983), 243-246.   DOI:10.1016/0167-6911(83)90021-x
  16. R. Olfati-Saber, J. Fax and R. Murray: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95 (2007), 215-233.   DOI:10.1109/jproc.2006.887293
  17. J. Peng and X. Ye: Cooperative control of multiple heterogeneous agents with unknown high-frequency-gain signs. Systems Control Lett. 68 (2014), 51-56.   DOI:10.1016/j.sysconle.2014.02.010
  18. W. Ren and R. W. Beard: Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications. Springer-Verlag, London 2008.   DOI:10.1007/978-1-84800-015-5
  19. A. Schaft: $L_2$-Gain and Passivity in Nonlinear Control. Springer-Verlag, New York 1999.   DOI:10.1007/978-1-4471-0507-7
  20. Y. Su and J. Huang: Cooperative adaptive output regulation for a class of nonlinear uncertain multi-agent systems with unknown leader. Systems Control Lett. 62 (2013), 461-467.   DOI:10.1016/j.sysconle.2013.02.013
  21. Y. Tang: Leader-following coordination problem with an uncertain leader in a multi-agent system. IET Control Theory Appl. 8 (2014), 773-781.   DOI:10.1049/iet-cta.2013.0869
  22. X. Wang, D. Xu and Y. Hong: Consensus control of nonlinear leader-follower multi-agent systems with actuating disturbances. Systems Control Lett. 73 (2014), 58-66.   DOI:10.1016/j.sysconle.2014.09.004
  23. X. Ye: Decentralized adaptive regulation with unknown high-frequency-gain signs. IEEE Trans. Automat. Control 44 (1999), 2072-2076.   DOI:10.1109/9.802918