doi:

DOI: 10.3724/SP.J.1004.2012.00357

Acta Automatica Sinica (自动化学报) 2012/38:3 PP.357-365

Dynamic Behavior of Multi-agent Systems with Distributed Sampled Control


Abstract:
This paper devotes to the study of coordinated control and dynamical behavior of multi-agent systems in digital communication network by means of graph theory, matrix analysis, and control theory. It is assumed that each agent of the system is described by a sampling dynamical system and is able to obtain the information of location coordinates of its neighbors by remote sensors. The system behavior depends on a linear distributed protocol in digital communication network. Thus, the whole multi-agent system can be considered as a hybrid dynamic system. Our results show that the multi-agent systems under consideration may appear three different dynamical behaviors, i.e., asymptotical aggregation, periodic oscillation, and divergence of agents. The dynamical behavior of the system depends not only on the algebraic characterization of the network topology but also on the dynamics of agents, as well as the sampling time period. Moreover, we give some algebraic criteria relevant to the system behavior. Examples show the effectiveness of our results.

Key words:Multi-agent systems, distributed protocol, sampling systems, consensus

ReleaseDate:2014-07-21 16:25:22

Funds:Supported by National Natural Science Foundation of China (60674046), Theory and Application of Differential Equations Foundation of Nanjing Audit University (202720035)



1 Fax J A, Murray R M. Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control, 2004, 49(9): 1465-1476

2 Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 2004, 49(9): 1520-1533

3 Xie G M, Wang L. Consensus control for a class of networks of dynamic agents. International Journal of Robust and Nonlinear Control, 2007, 17(10-11): 941-959

4 Lin P, Jia Y M. Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies. IEEE Transactions on Automatic Control, 2010, 55(3): 778-784

5 Wang L, Xiao F. Finite-time consensus problems for networks of dynamic agents. IEEE Transactions on Automatic Control, 2010, 55(4): 950-955

6 Liu X W, Lu W L, Chen T P. Consensus of multi-agent systems with unbounded time-varying delays. IEEE Transactions on Automatic Control, 2010, 55(10): 2396-2401

7 Hong Y G, Chen G R, Bushnell L. Distributed observers design for leader-following control of multi-agent networks. Automatica, 2008, 44(3): 846-850

8 Olfati-Saber R, Fax J A, Murray R M. Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 2007, 95(1): 215-233

9 Hou Z G, Cheng L, Tan M. Decentralized robust adaptive control for the multiagent system consensus problem using neural networks. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2009, 39(3): 636-647

10 Meng Z Y, Ren W, Cao Y C, You Z. Leaderless and leader-following consensus with communication and input delays under a directed network topology. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2011, 41(1): 75-88

11 Lin Z Y, Francis B, Maggiore M. Necessary and sufficient graphical conditions for formation control of unicycles. IEEE Transactions on Automatic Control, 2005, 50(1): 121-127

12 Yu W W, Chen G R, Cao M, Kurths J. Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2010, 40(3): 881-891

13 Ren W. On consensus algorithms for double-integrator dynamics. IEEE Transactions on Automatic Control, 2008, 58(6): 1503-1509

14 Savkin A V. Coordinate collective motion of groups of autonomous mobile robots: analysis of vicsek's model. IEEE Transactions on Automatic Control, 2004, 49(6): 981-982

15 Liu Y, Passino K M, Polycarpou M. Stability analysis of one-dimensional asynchronous swarms. IEEE Transactions on Automatic Control, 2003, 48(10): 1848-1854

16 Xiao F, Wang L, Wang A. Consensus problems in discrete-time multiagent systems with fixed topology. Journal of Mathematical Analysis and Applications, 2006, 322(2): 587-598

17 Ren W, Cao Y C. Convergence of sampled-data consensus algorithms for double-integrator dynamics. In: Proceedings of the 47th IEEE Conference on Decision and Control. Cancun, Mexico: IEEE, 2008. 3965-3970

18 Cao Y C, Ren W, Li Y. Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication. Automatica, 2009, 45(5): 1299-1305

19 GaoY P, Wang L, Xie G M, Wu B. Consensus of multi-agent systems based on sampled-data control. International Journal of Control, 2009, 82(12): 2193-2205

20 Xie G M, Liu H Y, Wang L, Jia Y M. Consensus in networked multi-agent systems via sampled-data control: fixed topology case. In: Proceedings of the American Control Conference. St. Louis, USA: IEEE, 2009. 3902-3907

21 Zhu M H, Martnez S. Discrete-time dynamic average consensus. Automatica, 2010, 46(2): 322-329

PDF