Distributed impulsive consensus of the multiagent system without velocity measurement.(English)Zbl 1421.93133

Summary: This paper deals with the distributed consensus of the multiagent system. In particular, we consider the case where the velocity (second state) is unmeasurable and the communication among agents occurs at sampling instants. Based on the impulsive control theory, we propose an impulsive consensus algorithm that extends some of our previous work to account for the lack of velocity measurement. By using the stability theory of the impulsive system, some necessary and sufficient conditions are obtained to ensure the consensus of the controlled multiagent system. It is shown that the control gains, the sampled period and the eigenvalues of Laplacian matrix of communication graph play key roles in achieving consensus. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed algorithm.

MSC:

 93D99 Stability of control systems 93A14 Decentralized systems 68T42 Agent technology and artificial intelligence 93C15 Control/observation systems governed by ordinary differential equations
Full Text:

References:

 [1] Xiao, F.; Wang, L.; Chen, J.; Gao, Y., Finite-time formation control for multi-agent systems, Automatica, 45, 11, 2605-2611, (2009) · Zbl 1180.93006 [2] Tanner, H. G.; Jadbabaie, A.; Pappas, G. J., Flocking in fixed and switching networks, IEEE Transactions on Automatic Control, 52, 5, 863-868, (2007) · Zbl 1366.93414 [3] Su, H.; Wang, X.; Lin, Z., Flocking of multi-agents with a virtual leader, IEEE Transactions on Automatic Control, 54, 2, 293-307, (2009) · Zbl 1367.37059 [4] Guan, Z.-H.; Liu, Z.-W.; Feng, G.; Wang, Y.-W., Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control, IEEE Transactions on Circuits and Systems I, 57, 8, 2182-2195, (2010) [5] Wang, Z.; Wang, Y.; Liu, Y., Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays, IEEE Transactions on Neural Networks, 21, 1, 11-25, (2010) [6] Shen, B.; Wang, Z.; Hung, Y., Distributed $$H_\infty$$-consensus filtering in sensor networks with multiple missing measurements: the finite-horizon case, Automatica, 46, 10, 1682-1688, (2010) · Zbl 1204.93122 [7] Yuan, D.; Xu, S.; Zhao, H., Distributed primal-dual subgradient method for multiagent optimization via consensus algorithms, IEEE Transactions on Systems, Man, and Cybernetics B, 41, 6, 1715-1724, (2011) [8] Vicsek, T.; Czirók, A.; Ben-Jacob, E.; Cohen, I.; Shochet, O., Novel type of phase transition in a system of self-driven particles, Physical Review Letters, 75, 6, 1226-1229, (1995) [9] Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, 48, 6, 988-1001, (2003) · Zbl 1364.93514 [10] Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301 [11] Cao, Y.; Yu, W.; Ren, W.; Chen, G., An overview of recent progress in the study of distributed multi-agent coordination, IEEE Transactions on Industrial Informatics, 9, 1, 427-438, (2013) [12] Liu, Y.; Ho, D. W. C.; Wang, Z., A new framework for consensus for discrete-time directed networks of multi-agents with distributed delays, International Journal of Control, 85, 11, 1755-1765, (2012) · Zbl 1253.93081 [13] Liu, Z.-W.; Guan, Z.-H.; Li, T.; Zhang, X.-H.; Xiao, J.-W., Quantized consensus of multi-agent systems via broadcast gossip algorithms, Asian Journal of Control, 14, 6, 1634-1642, (2012) · Zbl 1303.93015 [14] Olfati-Saber, R.; Fax, J.; Murray, R., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 1, 215-233, (2007) · Zbl 1376.68138 [15] Lin, P.; Jia, Y., Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies, Automatica, 45, 9, 2154-2158, (2009) · Zbl 1175.93078 [16] Hu, Y.; Su, H.; Lam, J., Adaptive consensus with a virtual leader of multiple agents governed by locally Lipschitz nonlinearity, International Journal of Robust and Nonlinear Control, 23, 9, 978-990, (2013) · Zbl 1270.93004 [17] Su, H.; Chen, G.; Wang, X.; Lin, Z., Adaptive second-order consensus of networked mobile agents with nonlinear dynamics, Automatica, 47, 2, 368-375, (2011) · Zbl 1207.93006 [18] Gao, Y.; Wang, L., Sampled-data based consensus of continuous-time multi-agent systems with time-varying topology, IEEE Transactions on Automatic Control, 56, 5, 1226-1231, (2011) · Zbl 1368.93424 [19] Li, T.; Zhang, J., Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle, Science in China F, 52, 11, 2089-2103, (2009) · Zbl 1182.93083 [20] Liu, H.; Xie, G.; Wang, L., Necessary and sufficient conditions for solving consensus problems of double-integrator dynamics via sampled control, International Journal of Robust and Nonlinear Control, 20, 15, 1706-1722, (2010) · Zbl 1204.93080 [21] Qin, J.; Gao, H., A sufficient condition for convergence of sampled-data consensus for double-integrator dynamics with nonuniform and time-varying communication delays, IEEE Transactions on Automatic Control, 57, 9, 2417-2422, (2012) · Zbl 1369.93043 [22] Qin, J.; Zheng, W.; Gao, H., Convergence analysis for multiple agents with double-integrator dynamics in a sampled-data setting, IET Control Theory & Applications, 5, 18, 2089-2097, (2011) [23] Qin, J.; Zheng, W. X.; Gao, H., Sampled-data consensus for multiple agents with discrete second-order dynamics, Proceedings of the 49th IEEE Conference on Decision and Control (CDC ’10), IEEE [24] Yu, W.; Zhou, L.; Yu, X.; Lu, J.; Lu, R., Consensus in multi-agent systems with second-order dynamics and sampled data, IEEE Transactions on Industrial Informatics, (2012) [25] Zhang, Y.; Tian, Y.-P., Consensus of data-sampled multi-agent systems with random communication delay and packet loss, IEEE Transactions on Automatic Control, 55, 4, 939-943, (2010) · Zbl 1368.94067 [26] Abdessameud, A.; Tayebi, A., On consensus algorithms for double-integrator dynamics without velocity measurements and with input constraints, Systems & Control Letters, 59, 12, 812-821, (2010) · Zbl 1217.93009 [27] Cao, Y.; Ren, W., Distributed coordinated tracking with reduced interaction via a variable structure approach, IEEE Transactions on Automatic Control, 57, 1, 33-48, (2012) · Zbl 1369.93012 [28] Hong, Y.; Hu, J.; Gao, L., Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 42, 7, 1177-1182, (2006) · Zbl 1117.93300 [29] Yu, W.; Zheng, W. X.; Chen, G.; Ren, W.; Cao, J., Second-order consensus in multi-agent dynamical systems with sampled position data, Automatica, 47, 7, 1496-1503, (2011) · Zbl 1220.93005 [30] Jiang, H.; Bi, Q.; Zheng, S., Impulsive consensus in directed networks of identical nonlinear oscillators with switching topologies, Communications in Nonlinear Science and Numerical Simulation, 17, 1, 378-387, (2012) · Zbl 1239.93004 [31] Liu, B.; Hill, D. J., Impulsive consensus for complex dynamical networks with nonidentical nodes and coupling time-delays, SIAM Journal on Control and Optimization, 49, 2, 315-338, (2011) · Zbl 1217.93078 [32] Wu, Q.; Zhou, J.; Xiang, L., Impulsive consensus seeking in directed networks of multi-agent systems with communication time delays, International Journal of Systems Science, 43, 8, 1479-1491, (2012) · Zbl 1417.93290 [33] Guan, Z.-H.; Liu, Z.-W.; Feng, G.; Jian, M., Impulsive consensus algorithms for second-order multi-agent networks with sampled information, Automatica, 48, 7, 1397-1404, (2012) · Zbl 1246.93007 [34] Liu, Z.-W.; Guan, Z.-H.; Shen, X.; Feng, G., Consensus of multi-agent networks with aperiodic sampled communication via impulsive algorithms using position-only measurements, IEEE Transactions on Automatic Control, 57, 10, 2639-2643, (2012) · Zbl 1369.93035 [35] Liu, Z.-W.; Guan, Z.-H.; Zhou, H., Impulsive consensus for leader-following multiagent systems with fixed and switching topology, Mathematical Problems in Engineering, 2013, (2013) [36] Bullo, F.; Cortés, J.; Martinez, S., Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms, (2009), Princeton University Press · Zbl 1193.93137 [37] Wu, C. W.; Chua, L. O., Synchronization in an array of linearly coupled dynamical systems, IEEE Transactions on Circuits and Systems I, 42, 8, 430-447, (1995) · Zbl 0867.93042
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.