Kybernetika 51 no. 4, 639-654, 2015

Distributed consensus control for discrete-time linear multi-agent systems with reduced-order observer

Wenhai Chen, Lixin Gao, Xiaole Xu and Bingbing XuDOI: 10.14736/kyb-2015-4-0639

Abstract:

In this paper, we investigate multi-agent consensus problem with discrete-time linear dynamics under directed interaction topology. By assumption that all agents can only access the measured outputs of its neighbor agents and itself, a kind of distributed reduced-order observer-based protocols are proposed to solve the consensus problem. A multi-step algorithm is provided to construct the gain matrices involved in the protocols. By using of graph theory, modified discrete-time algebraic Riccati equation and Lyapunov method, the proposed protocols can be proved to solve the discrete-time consensus problem. Furthermore, the proposed protocol is generalized to solve the model-reference consensus problem. Finally, a simulation example is given to illustrate the effectiveness of our obtained results.

Keywords:

observer, discrete-time system, multi-agent system, consensus, distributed control

Classification:

93A14, 93C10

paper.pdf

References:

  1. Y. Cao, W. Yu, W. Ren and G. Chen: An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans. Industr. Informatics 9 (2013), 427-4384.   DOI:10.1109/tii.2012.2219061
  2. C. T. Chen: Linear System Theory and Design. Third edition. Oxford University Press, New York 1999.   CrossRef
  3. M. Franceschetti, K. Poolla, M. Jordan and S. Sastry: Kalman filtering with intermittent observations. IEEE Trans. Automat. Control 49 (2004), 1453-1464.   DOI:10.1109/tac.2004.834121
  4. 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
  5. L. Gao, C. Tong and L. Wang: $H_\infty$ dynamic output feedback consensus control for discrete-time multi-agent systems with switching topology. The Arabian J. Sci. Engrg. 39 (2014), 1477-1487.   CrossRef
  6. Y. Gao and L. Wang: Consensus of multiple dynamic agents with sampled information. IET Control Theory Appl. 4 (2010), 945-956.   CrossRef
  7. L. Gao, B. Xu, J. Li and H. Zhang: Distributed reduced-order observer-based approach to consensus problems for linear multi-agent systems. IET Control Theory Appl. 9 (2015), 784-792.   CrossRef
  8. L. Gao, X. Zhu and W. Chen: Leader-following consensus problem with an accelerated motion leader. Int. J. Control, Automation, and Systems 10 (2012), 5, 931-939.   DOI:10.1007/s12555-012-0509-z
  9. K. Hengster-Movric and F. Lewis: Cooperative observers and regulators for discrete-time multiagent systems. Int. J. Robust and Nonlinear Control 23 (2013), 1545-1562.   DOI:10.1002/rnc.2840
  10. K. Hengster-Movric, K. You, F. L. Lewis and L. Xie: Synchronization of discrete-time multi-agent systems on graphs using Riccati design. Automatica 49 (2013), 414-423.   DOI:10.1016/j.automatica.2012.11.038
  11. 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
  12. Y. Hong, G. Chen and L. Bushnell: Distributed observers design for leader-following control of multi-agent networks. Automatica 44 (2008), 846-850.   DOI:10.1016/j.automatica.2007.07.004
  13. Y. Hong and X. Wang: Multi-agent tracking of a high-dimensional active leader with switching topology. J. Systems Science Complex. 22 (2009), 722-731.   DOI:10.1007/s11424-009-9197-z
  14. J. Hu, J. Geng and H. Zhou: An observer-based consensus tracking control and application to event-triggered tracking. Comm. Nonlinear Sci. Numer. Simul. 20 (2015), 559-570.   DOI:10.1016/j.cnsns.2014.06.002
  15. J. Hu and W. Zheng: Adaptive tracking control of leader follower systems with unknown dynamics and partial measurements. Automatica 50 (2014), 1416-1423.   DOI:10.1016/j.automatica.2014.02.037
  16. A. Jadbabaie, J. Lin and A. S. Morse: Coordination of groups of mobile agents using nearest neighbor rules. IEEE Trans. Automat. Control 48 (2003), 988-1001.   DOI:10.1109/tac.2003.812781
  17. Y. Ke and L. Xie: Network topology and communication data rate for consensusability of discrete-time multi-agent systems. IEEE Trans. Automat. Control 56 (2011), 2262-2275.   DOI:10.1109/tac.2011.2164017
  18. Z. Li, Z. Duan, G. Chen and L. Huang: Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint. IEEE Trans. on Circuits and Systems I: Regular Papers 57 (2010), 213-224.   DOI:10.1109/tcsi.2009.2023937
  19. Z. Li, X. Liu, P. Lin and W. Ren: Consensus of linear multi-agent systems with reduced-order observer-based protocols. Systems Control Lett. 60 (2011), 510-516.   DOI:10.1016/j.sysconle.2011.04.008
  20. Y. Liu, D. W. C. Ho and Z. Wang: A new framework for consensus for discrete-time directed networks of multi-agents with distributed delays. Int. J. Control 85 (2012), 1755-1765.   DOI:10.1080/00207179.2012.703331
  21. R. Olfati-Saber and R. M. Murrary: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control. 49 (2004), 1520-1533.   DOI:10.1109/tac.2004.834113
  22. W. Ren and Y. Cao: Distributed Coordination of Multi-agent Networks. Springer-Verlag London Limited 2011.   DOI:10.1007/978-0-85729-169-1
  23. Y. Su and J. Huang: Two consensus problems for discrete-time multi-agent systems with switching network topology. Automatica 48 (2012), 1988-1997.   DOI:10.1016/j.automatica.2012.03.029
  24. B. Xu, L. Gao, Y. Zhang and X. Xu: Leader-following consensus stability of discrete-time linear multiagent systems with observer-based protocols. Abstract and Applied Analysis 2013 (2013), 1-10.   DOI:10.1155/2013/357971
  25. B. Xu, J. Li and L. Gao: Distributed reduced-order observer-based consensus control of discrete-time linear multi-agent system. In: Proc. 3rd IFAC International Conference on Intelligent Control and Automation Science, 2013, pp. 124-129.   DOI:10.3182/20130902-3-cn-3020.00040
  26. X. Xu, S. Chen, W. Huang and L. Gao: Leader-following consensus of discrete-time multi-agent systems with observer-based protocols. Neurocomputing 118 (2013), 334-341.   DOI:10.1016/j.neucom.2013.02.023
  27. X. Xu, S. Chen and L. Gao: Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design. Neurocomputing 156 (2015), 297-305.   DOI:10.1016/j.neucom.2014.12.037
  28. C. Zhai: Sweep coverage of discrete time multi-robot networks with general topologies. Kybernetika 50 (2014), 19-31.   CrossRef
  29. H. Zhang, F. L. Lewis and A. Das: Optimal design for synchronization of cooperative systems: State feedback, observer and output feedback. IEEE Trans. Automat. Control 56 (2011), 1948-1952.   DOI:10.1109/tac.2011.2139510