×

Delay-dependent admissible consensualization for singular time-delayed swarm systems. (English) Zbl 1252.93006

Summary: Admissible consensus analysis and design problems for high-order linear time-invariant singular swarm systems with time delays are investigated. Firstly, by state decomposition, the admissible consensus problem is transformed into admissible problems of multiple singular subsystems with lower dimensions. Then, Linear Matrix Inequality (LMI) criteria for admissible consensualization are presented, which only involve eight LMI constraints independent of the number of agents. Moreover, an explicit expression of the consensus function which is independent of time delays is presented, and the impacts of protocol states and interaction topologies on the consensus function are revealed. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.

MSC:

93A14 Decentralized systems
93C05 Linear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
93B52 Feedback control

Software:

LMI toolbox
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Vicsek, T.; Czirók, A.; Ben-Jacob, E.; Cohen, I.; Shochet, O., Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75, 6, 1226-1229 (1995)
[2] Czirók, A.; Vicsek, T., Collective behavior of interacting self-propelled particles, Physica A, 281, 11, 17-29 (2000)
[3] Olfati-Saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE Trans. Automat. Control, 51, 3, 401-420 (2006) · Zbl 1366.93391
[4] Fax, J. A.; Murray, R. M., Information flow and cooperative control of vehicle formations, IEEE Trans. Automat. Control, 49, 9, 1465-1476 (2004) · Zbl 1365.90056
[5] 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
[6] Cai, N.; Zhong, Y., Formation controllability of high-order linear time-invariant swarm systems, IET Control Theory Appl., 4, 4, 646-654 (2010)
[7] Abdessameud, A.; Tayebi, A., Attitude synchronization of a group of spacecraft without velocity measurements, IEEE Trans. Automat. Control, 54, 11, 2642-2648 (2009) · Zbl 1367.93413
[8] Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automat. Control, 48, 6, 988-1001 (2003) · Zbl 1364.93514
[9] Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automat. Control, 49, 9, 1520-1533 (2004) · Zbl 1365.93301
[10] Ren, W.; Beard, R. W., Consensus seeking in multi-agent systems under dynamically changing interaction topologies, IEEE Trans. Automat. Control, 50, 5, 655-661 (2005) · Zbl 1365.93302
[11] Blimana, P. A.; Ferrari-Trecate, G., Average consensus problems in networks of agents with delayed communications, Automatica, 44, 8, 1985-1995 (2008) · Zbl 1283.93013
[12] Sun, Y. G.; Wang, L.; Xie, G., Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays, Systems Control Lett., 57, 2, 175-183 (2008) · Zbl 1133.68412
[13] Lin, P.; Jia, Y., Average consensus in networks of multi-agents with both switching topology and coupling time-delay, Physica A, 387, 1, 303-313 (2008)
[14] Sun, Y. G.; Wang, L., Consensus of multi-agent systems in directed networks with nonuniform time-varying delays, IEEE Trans. Automat. Control, 54, 7, 1607-1613 (2009) · Zbl 1367.93574
[15] Chopra, N.; Spong, M. W.; Lozano, R., Synchronization of bilateral teleoperators with time delay, Automatica, 44, 8, 2142-2148 (2008) · Zbl 1283.93094
[16] I. Lestas, G. Vinnicombe, The \(S\); I. Lestas, G. Vinnicombe, The \(S\)
[17] U. Münz, A. Papachristodoulou, F. Allgöwer, Generalized Nyquist consensus condition for high-order linear multi-agent systems with communication delays, in: Proc. IEEE Conf. Decision and Control, 2009 pp. 4765-4771.; U. Münz, A. Papachristodoulou, F. Allgöwer, Generalized Nyquist consensus condition for high-order linear multi-agent systems with communication delays, in: Proc. IEEE Conf. Decision and Control, 2009 pp. 4765-4771.
[18] Xi, J.; Shi, Z.; Zhong, Y., Consensus analysis and design for high-order linear swarm systems with time-varying delays, Physica A, 390, 23, 4114-4123 (2011)
[19] W. Dong, J. Xi, Z. Shi, Y. Zhong, Consensus for high-order time-delayed swarm systems with uncertainties and external disturbances, in: Proc. Chinese Control Conf., 2011, pp. 22-24.; W. Dong, J. Xi, Z. Shi, Y. Zhong, Consensus for high-order time-delayed swarm systems with uncertainties and external disturbances, in: Proc. Chinese Control Conf., 2011, pp. 22-24.
[20] Gao, H.; Lam, J.; Wang, C.; Wang, Y., Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay, IET Control Theory Appl., 151, 6, 691-698 (2004)
[21] Chen, W. H.; Guan, Z. H.; Lu, X., Delay-dependent output feedback guaranteed cost control for uncertain time-delay systems, Automatica, 40, 7, 1263-1268 (2004) · Zbl 1056.93040
[22] He, Y.; Wu, M.; Liu, G. P.; She, J. H., Output feedback stabilization for a discrete-time system with a time-varying delay, IEEE Trans. Automat. Control, 53, 10, 2372-2377 (2008) · Zbl 1367.93507
[23] Dai, L., Singular Control Systems (1989), Springer: Springer Berlin
[24] Xu, S.; Van Dooren, P.; Stefan, R.; Lam, J., Robust stability and stabilization for singular systems with state delay and parameter uncertainty, IEEE Trans. Automat. Control, 47, 7, 1122-1128 (2002) · Zbl 1364.93723
[25] Masubuchi, I.; Kamitane, Y.; Ohara, A.; Suda, N., \(H_\infty\) control for descriptor systems: a matrix inequalities approach, Automatica, 33, 4, 669-673 (1997) · Zbl 0881.93024
[26] Wu, Z.; Zhou, W., Delay-dependent robust \(H_\infty\) control for uncertain singular time-delay systems, IET Control Theory Appl., 1, 5, 1234-1241 (2007)
[27] X.R. Yang, G.P. Liu, Necessary and sufficient consensus conditions of descriptor multi-agent systems, IEEE Trans. Circuits and Systems I (2012) (in press), Reg. Papers, Online available.; X.R. Yang, G.P. Liu, Necessary and sufficient consensus conditions of descriptor multi-agent systems, IEEE Trans. Circuits and Systems I (2012) (in press), Reg. Papers, Online available.
[28] S. Ma, S. Hackwood, G. Beni, Multi-agent supporting systems (MASS): control with centralized estimator of disturbance, in: Proceedings IEEE/RSJ International Conf. Intelligent Robots and Systems, 1994, pp. 679-686.; S. Ma, S. Hackwood, G. Beni, Multi-agent supporting systems (MASS): control with centralized estimator of disturbance, in: Proceedings IEEE/RSJ International Conf. Intelligent Robots and Systems, 1994, pp. 679-686.
[29] Xi, J.; Shi, Y.; Zhong, Y., Consensus and consensualization of high-order linear time-invariant singular swarm systems, Physica A, 391, 23, 5839-5849 (2012)
[30] J. Xi, F. Meng, Z. Shi, Y. Zhong, Admissible consensualization for singular swarm systems with time delays, in: Proceedings Chinese Control Conf., 2012, pp. 6285-6291.; J. Xi, F. Meng, Z. Shi, Y. Zhong, Admissible consensualization for singular swarm systems with time delays, in: Proceedings Chinese Control Conf., 2012, pp. 6285-6291.
[31] J. Xi, Z. Shi, Y. Zhong, Consensus and consensualization of high-order swarm systems with time delays and external disturbances, J. Dyn. Syst. Meas. Control (2011) (in press).; J. Xi, Z. Shi, Y. Zhong, Consensus and consensualization of high-order swarm systems with time delays and external disturbances, J. Dyn. Syst. Meas. Control (2011) (in press).
[32] Xi, J.; Cai, N.; Zhong, Y., Consensus problems for high-order linear time-invariant swarm systems, Physica A, 389, 24, 5619-5627 (2010)
[33] Godsil, C.; Royal, G., Algebraic Graph Theory (2001), Springer-Verlag: Springer-Verlag New York
[34] Boyd, S.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (1994), SIAM: SIAM Philadelphia, PA · Zbl 0816.93004
[35] Xie, L.; de Souza, C. E., Robust \(H_\infty\) control for linear systems with norm-bounded time-varying uncertainty, IEEE Trans. Automat. Control, 37, 8, 1188-1191 (1992) · Zbl 0764.93027
[36] Ghaoui, L. E.; Oustry, F.; Aitrami, M., A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Trans. Automat. Control, 42, 8, 1171-1176 (1997) · Zbl 0887.93017
[37] Gahinet, P.; Nemirovskii, A.; Laub, A. J.; Chilali, M., LMI Control Toolbox User’s Guide (1995), The Math Works: The Math Works Natick, MA
[38] Xiao, F.; Wang, L., Consensus problems for high-dimensional multi-agent systems, IET Control Theory Appl., 1, 3, 830-837 (2007)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.