# zbMATH — the first resource for mathematics

Event-triggered tracking control for heterogeneous multi-agent systems with Markov communication delays. (English) Zbl 1293.93066
Summary: In this paper, we investigate the consensus problem of a set of discrete-time heterogeneous multi-agent systems with random communication delays represented by a Markov chain, where the multi-agent systems are composed of two kinds of agents differed by their dynamics. First, distributed consensus control is designed by employing the event-triggered communication technique, which can lead to a significant reduction of the information communication burden in the multi-agent network. Then, the mean square stability of the closed loop multi-agent systems is analyzed based on the Lyapunov functional method and the Kronecker product technique. Sufficient conditions are obtained to guarantee the consensus in terms of linear matrix inequalities (LMIs). Finally, a simulation example is given to illustrate the effectiveness of the developed theory.

##### MSC:
 93A14 Decentralized systems 68T42 Agent technology and artificial intelligence 93C55 Discrete-time control/observation systems 93E03 Stochastic systems in control theory (general) 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
Full Text:
##### References:
 [1] Su, H.; Wang, X.; Lin, Z., Flocking of multi-agents with a virtual leader, IEEE Transactions on Automatic Control, 54, 293-307, (2009) · Zbl 1367.37059 [2] Ren, W.; Beard, R.; Atkins, E., Information consensus in multivehicle cooperative control, IEEE Control Systems Magazine, 27, 293-307, (2007) [3] Liu, S.; Xie, L.; Zhang, H., Distributed consensus for multi-agent systems with delays and noises in transmission channels, Automatica, 47, 920-934, (2011) · Zbl 1233.93007 [4] Su, H.; Wang, X.; Lin, Z., Synchronization of coupled harmonic oscillators in a dynamic proximity network, Automatica, 45, 2286-2291, (2009) · Zbl 1179.93102 [5] Su, H.; Wang, X.; Chen, G., Rendezvous of multiple mobile agents with preserved network connectivity, Systems & Control Letters, 59, 313-322, (2010) · Zbl 1191.93005 [6] Ren, W.; Atkins, E., Distributed multi-vehicle coordinated control via local information exchange, International Journal of Robust and Nonlinear Control, 17, 1002-1033, (2007) · Zbl 1266.93010 [7] Yu, W.; Chen, G.; Cao, M.; Kurths, J., Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics, IEEE Transactions on Systems, Man, and Cybernetics, Part BCybernetics, 40, 881-891, (2010) [8] Guan, Z.; Wu, Y.; Feng, G., Control theory and systems-consensus analysis based on impulsive systems in multiagent networks, IEEE Transactions on Circuits and Systems-I—Regular Papers, 59, 170-178, (2012) [9] Tian, Y.; Liu, C., Consensus of multi-agent systems with diverse input and communication delays, IEEE Transactions on Automatic Control, 53, 2122-2128, (2008) · Zbl 1367.93411 [10] Lin, P.; Jia, Y., Brief papermulti-agent consensus with diverse time-delays and jointly-connected topologies, Automatica, 47, 848-856, (2011) · Zbl 1215.93013 [11] Zhou, W.; Wang, T.; Mou, J.; Fang, J., Mean square exponential synchronization in Lagrange sense for uncertain complex dynamical networks, Journal of the Franklin Institute, 349, 1267-1282, (2012) · Zbl 1273.93017 [12] Sun, Y., Average consensus in networks of dynamic agents with uncertain topologies and time-varying delays, Journal of the Franklin Institute, 349, 1061-1073, (2012) · Zbl 1273.93009 [13] Lin, P.; Qin, K.; Zhao, H.; Sun, M., A new approach to average consensus problems with multiple time-delays and jointly-connected topologies, Journal of the Franklin Institute, 349, 293-304, (2012) · Zbl 1254.93009 [14] M. Cao, A. Morse and B. Anderson, Reaching an agreement using delayed information, in: 2006 45th IEEE Conference on Decision and Control, 2006, pp. 3375-3380. [15] Sun, Y.; Wang, L., Consensus of multi-agent systems in directed networks with nonuniform time-varying delays, IEEE Transactions on Automatic Control, 54, 1607-1613, (2009) · Zbl 1367.93574 [16] D. Liu, C. Liu, Consensus problem of discrete-time second-order multi-agent network with communication delays, in: Third International Symposium on Intelligent Information Technology Application, vol. 2, 2009, pp. 340-344. [17] Meng, D.; Jia, Y.; Du, J.; Yu, F., Tracking control over a finite interval for multi-agent systems with a time-varying reference trajectory, Systems & Control Letters, 61, 807-818, (2012) · Zbl 1250.93013 [18] S. Yang, J. Xu, Adaptive Iterative learning control for multi-agent systems consensus tracking, in: 2012 IEEE International Conference on Systems, Man, and Cybernetics (SMC), 2012, pp. 2803-2808. [19] Yu, W.; Zheng, W.; Chen, G.; Ren, W.; Cao, J., Second-order consensus in multi-agent dynamical systems with sampled position data, Automatica, 47, 1496-1503, (2011) · Zbl 1220.93005 [20] Su, H.; Chen, G.; Wang, X.; Lin, Z., Adaptive second-order consensus of networked mobile agents with nonlinear dynamics, Automatica, 47, 368-375, (2011) · Zbl 1207.93006 [21] Olfati-Saber, R.; Fax, J.; Murray, R., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 215-233, (2007) · Zbl 1376.68138 [22] Dimarogonas, D.; Frazzoli, E.; Johansson, K., Distributed event-triggered control for multi-agent systems, IEEE Transactions on Automatic Control, 57, 1291-1297, (2012) · Zbl 1369.93019 [23] Hu, S.; Yue, D., Event-triggered control design of linear networked systems with quantizations, ISA Transactions, 51, 153-162, (2012) [24] G. Seyboth, Event-based Control for Multi-Agent Systems, Master’s Degree Project, Stockholm, Sweden, 2010. [25] D. Dimarogonas, K. Johansson, Event-triggered control for multi-agent systems, in: 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, 2009, pp. 7131-7136. [26] Hu, J.; Chen, G.; Li, H., Distributed event-triggered tracking control of leader-follower multi-agent systems with communication delays, Kybernetika, 47, 630, (2011) · Zbl 1227.93008 [27] Liu, Z.; Chen, Z., Reaching consensus in networks of agents via event-triggered control, Journal of Information & Computational Science, 8, 393-402, (2011) [28] Tabuada, P., Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 52, 1680-1685, (2007) · Zbl 1366.90104 [29] Zheng, Y.; Zhu, Y.; Wang, L., Consensus of heterogeneous multi-agent systems, IET Control Theory & Applications, 5, 1881-1888, (2011) [30] Liu, C.; Liu, F., Stationary consensus of heterogeneous multi-agent systems with bounded communication delays, Automatica, 47, 2130-2133, (2011) · Zbl 1227.93010 [31] Kim, H.; Shim, H.; Seo, J., Output consensus of heterogeneous uncertain linear multi-agent systems, IEEE Transactions on Automatic Control, 56, 200-206, (2011) · Zbl 1368.93378 [32] Y. Tian, High-order consensus of heterogeneous multi-agent systems, in: 2011 8th Asian Control Conference (ASCC), 2011, pp. 341-346. [33] Wu, J.; Shi, Y., Consensus in multi-agent systems with random delays governed by a Markov chain, Systems & Control Letters, 60, 863-870, (2011) · Zbl 1226.93015 [34] Feng, J.; Lam, J.; Shu, Z., Stabilization of Markovian systems via probability rate synthesis and output feedback, IEEE Transactions on Automatic Control, 55, 773-777, (2010) · Zbl 1368.93535 [35] Wang, X.; Lemmon, M., Event-triggering in distributed networked control systems, IEEE Transactions on Automatic Control, 56, 586-601, (2011) · Zbl 1368.93211 [36] Yook, J.; Tilbury, D.; Soparkar, N., Trading computation for bandwidthreducing communication in distributed control systems using state estimators, IEEE Transactions on Control Systems Technology, 10, 503-518, (2002) [37] Liu, C.; Liu, F., Asynchronously-coupled consensus of second-order dynamic agents with communication delay, International Journal of Innovative Computing, Information and Control, 6, 5035-5046, (2010) [38] Hu, S.; Yue, D.; Liu, J., $$h_\infty$$ filtering for networked systems with partly known distribution transmission delays, Information Sciences, 194, 270-282, (2012) · Zbl 1248.93164 [39] Y. Hu, H. Su, J. Lam, Adaptive consensus with a virtual leader of multiple agents governed by locally Lipschitz nonlinearity, International Journal of Robust and Nonlinear Control (2012) http://dx.doi.org/10.1002/rnc.2811. · Zbl 1270.93004 [40] Ko, J.; Park, P., Delay-dependent stability criteria for systems with asymmetric bounds on delay derivative, Journal of the Franklin Institute, 348, 2674-2688, (2011) · Zbl 1239.93089 [41] Lou, X.; Ye, Q.; Cui, B., Parameter-dependent robust stability of uncertain neural networks with time-varying delay, Journal of the Franklin Institute, 349, 1891-1903, (2012) · Zbl 1254.93128 [42] Chiou, J.; Wang, C.; Cheng, C., On delay-dependent stabilization analysis for the switched time-delay systems with the state-driven switching strategy, Journal of the Franklin Institute, 348, 261-276, (2011) · Zbl 1218.34091
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.