Consensus of Nonlinear Multi-Agent Systems with Exogenous Disturbances

Xiaozhi Yu, Zhen He, Feng Yu

2015

Abstract

Most existing research concerning the consensus problem of multi-agent systems has been focused on linear first-order or two-order systems without disturbances. However, in practice, most multi-agent systems are complicated nonlinear system subjected to disturbances. In this paper, the coordinated tracking problem for nonlinear undirected multi-agent systems with exogenous disturbances is studied in the framework of consensus theory. The exogenous disturbances generated by both linear exosystems and nonlinear exosystems are considered. Disturbance observers are developed to estimate the disturbances generated by the linear exogenous systems. The Lyapunov stability theorem is used to prove the asymptotical consensus of the systems. The dynamic gain technique is used to construct the disturbance observer for the disturbance generated by a nonlinear exosystem. Based on the adaptive disturbance observer, a consensus protocol is proposed for the nonlinear multi-agent system. Finally, the proposed design approaches are verified though simulation examples.

References

  1. Bliman, P. A. and Ferrari, T. G., 2008. Average consensus problems in networks of agents with delayed communications. Automatic, vol. 44, pp.1985-1995.
  2. Corts, J., Martinez, S. and Bullo, F., 2005. Spatiallydistributed coverage optimization and control with limited-range interactions. ESAIM. Control, Optimization and Calculus of Variations, vol. 11, pp. 691-719.
  3. Chen, W. H., 2004. Disturbance observer based control for nonlinear systems. Mechatronics, IEEE/ASME Transaction on vol. 9, no.4, pp.706-710.
  4. Das, A. and Lewis, F. L., 2011. Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities. International Journal of Robust and Nonlinear Control, vol. 21, pp. 1509-1524.
  5. Hu, J. P., Hong, Y. G. and Feng, G., 2008. Distributed dynamic control for leaderless multi-agent consensus with star-like topology. Asian Journal of Control, vol. 10, no. 2, pp.233-237.
  6. Konduri, S., Pagilla, P. R. and Darbha, S., 2013. Vehicle formations using directed information flow graphs. American Control Conference (ACC), pp.3045, 3050, 17-19.
  7. Khalil, H., 2002. Nonlinear Systems, Upper Saddle River, USA: Prentice-Hall, 3nd edition.
  8. Liu Y., Passino, K. M. and Polycarpou, M. M., 2003. Stability analysis of m-dimensional asynchronous swarms with a fixed communication topology. IEEE Transactions on Automatic Control, vol. 48, no. 1, pp.76-95.
  9. Mei, J., Ren, W. and Ma, G. F., 2011. Distributed coordinated tracking with a dynamic leader for multiple Euler-Lagrange systems [J]. IEEE Transactions on Automatic Control, pp. 1415-1421.
  10. MA, G. F. and Mei, J., 2011. Coordinated tracking for nonlinear multi-agent systems under directed network. Control and Decision, vol. 26, no. 12, pp. 1861-1865.
  11. Ren, W. and Atkins, E., 2007. Distributed multi-vehicle coordinated control via locial information exchange. International Journal of Robust and Nonlinear Control, vol. 17, pp. 1002-1033.
  12. Ren, W., 2007. Distributed attitude alignment in spacecraft formation flying [J]. International Journal of Adaptive Control and Signal Processing, pp. 95-113.
  13. Sepulchre, R., Paley, D. A. and Leonard, N. E., 2008. Stabilization of planar collective motion with limited communication [J]. IEEE Transactions on Automatic Control, pp. 706-719.
  14. Tanner, H. G., Jadbabaie, A. and Pappas, G. J., 2007. Flocking in fixed and switching networks. IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 863-868.
  15. Wu, C. W., 2005. Synchronization in networks of nonlinear dynamical systems coupled via a directed graph [J]. Nonlinearity, pp. 1057-1064.
  16. Xie, G. M. and Wang, L., 2007. Consensus control for a class of networks of dynamic agents. International Journal of Robust and Nonlinear Control, vol. 17, pp. 941-956.
  17. Yu, W. W., Chen, G. and Cao, M., 2010. Second-order consensus for multi-agent systems with directed topologies and nonlinear dynamics [J]. IEEE Transactions on Systems Man and Cybernetics-Part, pp. 881-891.
  18. Yang, H., Zhang, Z. and Zhang, S., 2011. Consensus of second-order multi-agent systems with exogenous disturbances. International Journal of Robust and Nonlinear Control, vol. 21, no. 9, pp. 945-956.
  19. Zhang, X. X. and Liu, X. P., 2013. Further results on consensus of second-order multi-agent systems with exogenous disturbance. IEEE Transaction on Circuits and Systems, vol. 60, no. 12, pp. 3215-3226.
Download


Paper Citation


in Harvard Style

Yu X., He Z. and Yu F. (2015). Consensus of Nonlinear Multi-Agent Systems with Exogenous Disturbances . In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-122-9, pages 281-286. DOI: 10.5220/0005566702810286


in Bibtex Style

@conference{icinco15,
author={Xiaozhi Yu and Zhen He and Feng Yu},
title={Consensus of Nonlinear Multi-Agent Systems with Exogenous Disturbances},
booktitle={Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2015},
pages={281-286},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005566702810286},
isbn={978-989-758-122-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Consensus of Nonlinear Multi-Agent Systems with Exogenous Disturbances
SN - 978-989-758-122-9
AU - Yu X.
AU - He Z.
AU - Yu F.
PY - 2015
SP - 281
EP - 286
DO - 10.5220/0005566702810286