AUTHORS: Kepeng Han, Dongmei Xie
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ABSTRACT: In this paper, we focus on studying the group consensus tracking issue of single-integrator and secondintegrator multi-agent systems with fixed communication topology and time delays under a pinning control protocol, respectively. For the former, We aim to propose some necessary and/or sufficient group consensus tracking conditions by using Lyapunov-Krasovskii function. For the latter, the observer-based bounded group consensus tracking control problem of second-order multi-agent systems in a disturbance environment is investigated, and some sufficient bounded group consensus tracking criteria are established. Moreover, this paper proposes a method of graph refactoring to find the relationship between the communication topology graph and matrix. Finally, numerical simulations are given to verify the effectiveness of our theoretical results.
KEYWORDS: Multi-agent systems, group consensus tracking, pinning control, Lyapunov-Krasovskii function, distributed observer.
REFERENCES:
[1] G. Q. Hu, Robust consensus tracking of a class of second-order multi-agent dynamic systems, Systems & Control Letters 61, 2012, pp. 134– 142.
[2] W. Ren, Consensus Tracking under directed interaction topologies: algorithms and experiments, American Control Conference, 2008, pp. 742–747.
[3] J. P. Hu, Y. G. Hong, Leader-following coordination of multi-agent systems with coupling time delays, Physica A 374, 2007, pp. 853–863.
[4] Z. Zahreddine and EF. Elshehawey On the stability of a system of differential equations with complex coefficients. Indian Journal of Pure and Applied Mathematics 19, 1988, pp. 963– 972.
[5] Z. J. Tang, T. Z. Huang, et al. Consensus of second-order multi-agent systems with nonuniform time-varying delays. Neurocomputing 97, 2012, pp. 410–414.
[6] Y. L. Cheng, D. M. Xie, Distributed observer design for bounded tracking control of leaderfollower multi-agent systems in a sampled-data setting, International Journal of Control 87, 2014, pp. 41–51.
[7] Y. G. Hong, G. R. Chen and L. Bushnell, Distributed observers design for leader-following control of multi-agent networks. Automatica 44, 2008, pp. 846–850.
[8] Y. G. Hong, J. P. Hu and L. X. Gao, Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42, 2006, PP. 1177–1182.
[9] J. Y. Yu, L. Wang, Group consensus in multiagent systems with switching topologies and communication delays, Systems & Control Letters 59, 2010, PP. 340–348.
[10] J. Y. Yu, L. Wang, Group consensus of multiagent systems with undirected communication graphs, Proceedings of the Asian Control Conference, 2009, pp. 105–110.
[11] J. Y. Yu, L. Wang, Group consensus of multiagent systems with directed information exchange, International Journal of Systems Science 43, 2012, pp. 334–348.
[12] J. Y. Yu, M. Yu, J. P. Hu, B. Liu, Group consensus in multi-agent systems with directed sampled data, Proceedings of the 32nd Chinese Control Conference, 2013, pp. 7168–7172.
[13] Y. Z. Feng, S. Y. Xu, B. Y. Zhang, Group consensus control for double-integrator dynamic multiagent systems with fixed communication topology, International Journal of Robust and Nonlinear Control 24, 2014, pp. 532–547.
[14] Q. Ma, Z. Wang, G. Y. Miao, Second-order group consensus for multi-agent systems via pinning leader-following approach, Journal of the Franklin Institute 351, 2014, pp. 1288–1300.
[15] X. F. Liao, L. H. Ji, On pinning group consensus for dynamical multiagent networks with general connected topology, Neurocomputing 135, 2014, pp. 262–267.
[16] W. W. Yu, J. D. Cao, Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays, Physics Letters A 351, 2006, pp. 64–78.
[17] S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM: Philadelphia, PA, 1994.
[18] I. Kovacs, DS. Silver and SG. Williams, Determinants of block matrices and Schurs formula, 1999.
[19] A. Ronger, R. Charles, Topics in Matrix Analysis, Cambridge Univ. Press, Cambridge, 1991.
[20] W. Rudin, Principles of Mathematical Analysis, New York, Auckland, Dusseldorf: McGraw-Hill Book Co, 1976.