×

Delay robustness in consensus problems. (English) Zbl 1204.93013

Summary: We investigate the robustness of consensus schemes for linear Multi-Agent Systems (MAS) to feedback delays. To achieve this, we develop a unified framework that considers linear MAS models with different feedback delays, e.g. affecting only the neighbor’s output, or affecting both the agent’s own and its neighbors’ output. This framework has the advantage of providing scalable, simple, and accurate set-valued conditions for consensus. Using these set-valued conditions, previous results on consensus in MAS with delays can be recovered and generalized. Moreover, we use them to derive conditions for the convergence rate of single integrator MAS with feedback delays. Finally, building on this framework, we propose a scalable delay-dependent design algorithm for consensus controllers for a large class of linear MAS.

MSC:

93A14 Decentralized systems
93C05 Linear systems in control theory
93B52 Feedback control
93B35 Sensitivity (robustness)

Software:

TRACE-DDE
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bliman, P.-A.; Ferrari-Trecate, G., Average consensus problems in networks of agents with delayed communications, Automatica, 44, 8, 1985-1995 (2008) · Zbl 1283.93013
[2] Brackstone, M.; McDonald, M., Car-following: a historical review, Transporation Research Part F, 2, 4, 181-196 (1999)
[4] Cao, M.; Morse, A. S.; Anderson, B. D.O., Reaching a consensus in a dynamically changing environment: a graphical approach & convergence ranges, measurement delays, and asynchronous events, SIAM Journal on Control and Optimization, 47, 2, 575-623 (2008) · Zbl 1157.93434
[5] Carli, R.; Bullo, F., Quantized coordination algorithms for rendezvous and deployment, SIAM Journal on Control and Optimization, 48, 3, 1251-1274 (2009) · Zbl 1192.68845
[6] Chopra, N.; Spong, M., Passivity-based control of multi-agent systems, (Kaxamura, S.; Svinin, M., Advances in robot control (2006), Springer: Springer Berlin, Germany), 107-134 · Zbl 1134.93308
[8] Desoer, C. A.; Wang, Y.-T., On the generalized Nyquist stability criterion, IEEE Transactions on Automatic Control, 25, 2, 187-196 (1980) · Zbl 0432.93039
[9] Fax, J. A.; Murray, R. M., Information flow and cooperative control of vehicle formations, IEEE Transactions on Automatic Control, 49, 9, 1465-1476 (2004) · Zbl 1365.90056
[10] Fiedler, Miroslav, Algebraic connectivity of graphs, Czechoslovak Mathematical Journal, 23, 2, 298-305 (1973) · Zbl 0265.05119
[12] Godsil, C.; Royle, G., Algebraic graph theory (2000), Springer: Springer New York, USA
[13] Gu, K.; Kharitonov, V. L.; Chen, J., Stability of time-delay systems (2003), Birkhäuser: Birkhäuser Boston · Zbl 1039.34067
[14] Horn, R. A.; Johnson, C. R., Matrix analysis (1985), Cambridge University Press: Cambridge University Press New York · Zbl 0576.15001
[15] Horn, R. A.; Johnson, C. R., Topics in matrix analysis (1991), Cambridge University Press: Cambridge University Press New York · Zbl 0729.15001
[18] Kao, C.-Y.; Jönsson, U.; Fujioka, H., Characterization of robust stability of a class of interconnected systems, Automatica, 45, 1, 217-224 (2009) · Zbl 1154.93409
[19] Kashyap, A.; Başar, T.; Srikant, R., Quantized consensus, Automatica, 43, 7, 1192-1203 (2007) · Zbl 1123.93090
[21] Lestas, I. C.; Vinnicombe, G., Scalable decentralized robust stability certificates for networks of interconnected heterogeneous dynamical systems, IEEE Transactions on Automatic Control, 51, 10, 1613-1625 (2006) · Zbl 1366.93468
[23] Lestas, I. C.; Vinnicombe, G., Scalable robust stability for nonsymmetric heterogeneous networks, Automatica, 43, 4, 714-723 (2007) · Zbl 1131.93040
[27] Mossaheb, S., A nyquist type stability criterion for linear multivariable delayed systems, International Journal of Control, 32, 5, 821-847 (1980) · Zbl 0461.93049
[30] Münz, U.; Papachristodoulou, A.; Allgöwer, F., Consensus reaching in multi-agent packet-switched networks, International Journal of Control, 82, 5, 953-969 (2009) · Zbl 1165.93025
[33] Münz, U.; Papachristodoulou, A.; Allgöwer, F., Robust rendezvous of heterogeneous Langrange systems on packet-switched networks, Automatisierungstechnik, 58, 4, 184-191 (2010)
[36] Olfati-Saber, R.; Fax, J. A.; Murray, R. M., Consensus and cooperation in networked multi-agent systems, Proceedings of IEEE, 95, 1, 215-233 (2007) · Zbl 1376.68138
[37] Olfati-Saber, R.; Murray, R. M., Consensus problem in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49, 9, 1520-1533 (2004) · Zbl 1365.93301
[39] Ren, W.; Beard, R. W., Distributed consensus in multi-vehicle cooperative control (2008), Springer: Springer London, UK · Zbl 1144.93002
[41] Skogestad, S.; Postlethwaite, I., Multivariable feedback control analysis and design (2004), Wiley: Wiley New York · Zbl 0842.93024
[42] Sun, Y. G.; Wang, L., Consensus of multi-agent systems in directed networks with nonuniform time-varying delays, IEEE Transactions on Automatic Control, 54, 7, 1607-1613 (2009) · Zbl 1367.93574
[43] Sun, Y. G.; Wang, L., Consensus problems in networks of agents with double-integrator dynamics and time-varying delays, International Journal of Control, 82, 10, 1937-1945 (2009) · Zbl 1178.93013
[44] Tian, Y.-P.; Liu, C.-L., Consensus of multi-agent systems with diverse input and communication delays, IEEE Transactions on Automatic Control, 53, 9, 2122-2128 (2008) · Zbl 1367.93411
[45] Toker, O.; Özbay, H., Complexity issues in robust stability of linear differential systems, Mathematics of Control, Signals, and Systems, 9, 4, 386-400 (1996) · Zbl 0878.93050
[48] Xiao, F.; Wang, L., Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE Transactions on Automatic Control, 53, 8, 1804-1816 (2008) · Zbl 1367.93255
[49] Xiao, F.; Wang, L., Consensus protocols for discrete-time multi-agent systems with time-varying delays, Automatica, 44, 10, 2577-2582 (2008) · Zbl 1155.93312
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.