Consensus of high-order multi-agent systems with large input and communication delays. (English) Zbl 1364.93044
Summary: We study in this paper the consensus problem for multi-agent systems with agents characterized by high-order linear systems with time delays in both the communication network and inputs. Provided that the open-loop dynamics of the agents is not exponentially unstable, but may be polynomially unstable, and the communication topology contains a directed spanning tree, a truncated predictor feedback approach is established to solve the consensus problem. It is shown that, if the delays are constant and exactly known, the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays. If it is further assumed that the open-loop dynamics of the agents only contains zero eigenvalues, the delays are allowed to be time-varying and unknown. Numerical examples are worked out to illustrate the effectiveness of the proposed approaches.
References:
| [1] | Chen, G. R.; Duan, Z. S., Network synchronizability analysis: a graph-theoretic approach, Chaos: An Interdisciplinary Journal of Nonlinear Science, 18, 3 (2008), 037102 · Zbl 1309.05166 |
| [2] | Duan, Z. S.; Chen, G. R.; Huang, L., Complex network synchronizability: analysis and control, Physical Review E, 76, 5, 056103 (2007) |
| [3] | Duan, Z.; Wang, J.; Chen, G.; Huang, L., Stability analysis and decentralized control of a class of complex dynamical networks, Automatica, 44, 4, 1028-1035 (2008) · Zbl 1283.93017 |
| [4] | Fax, J.; Murray, R., Information flow and cooperative control of vehicle formations, IEEE Transactions on Automatic Control, 49, 9, 1465-1476 (2004) · Zbl 1365.90056 |
| [6] | Hale, J., Theory of functional differential equations (1977), Springer-Verlag · Zbl 0352.34001 |
| [7] | Hong, Y.; Chen, G.; Bushnell, L., Distributed observers design for leader-following control of multi-agent networks, Automatica, 44, 3, 846-850 (2006) · Zbl 1283.93019 |
| [8] | Ishii, H.; Tempo, R., Distributed randomized algorithms for the PageRank computation, IEEE Transactions on Automatic Control, 55, 9, 1987-2002 (2010) · Zbl 1368.68045 |
| [9] | Ishii, H.; Tempo, R.; Bai, E.-W., A web aggregation approach for distributed randomized PageRank algorithms, IEEE Transactions on Automatic Control (2012) · Zbl 1369.93695 |
| [10] | Li, Z.; Duan, Z.; Chen, G.; Huang, L., Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint, IEEE Transactions on Circuits and Systems I: Regular Papers, 57, 1, 213-224 (2010) · Zbl 1468.93137 |
| [11] | Li, Q.; Jiang, Z. P., Global analysis of multi-agent systems based on Vicsek’s model, IEEE Transactions on Automatic Control, 54, 12, 2876-2881 (2009) · Zbl 1367.93369 |
| [12] | Li, Z.; Liu, X.; Lin, P.; Ren, W., Consensus of linear multi-agent systems with reduced-order observer-based protocols, Systems & Control Letters, 60, 7, 510-516 (2011) · Zbl 1222.93013 |
| [13] | Li, T.; Xie, L., Distributed consensus over digital networks with limited bandwidth and time-varying topologies, Automatica, 47, 9, 2006-2015 (2011) · Zbl 1227.93009 |
| [15] | Liu, X.; Lu, W.; Chen, T., Consensus of multi-agent systems with unbounded time-varying delays, IEEE Transactions on Automatic Control, 55, 10, 2396-2401 (2010) · Zbl 1368.93470 |
| [18] | Manitius, A.; Olbrot, A., Finite spectrum assignment problem for systems with delays, IEEE Transactions on Automatic Control, 24, 4, 541-552 (1979) · Zbl 0425.93029 |
| [19] | Munz, U.; Papachristodoulou, A.; Allgower, F., Delay robustness in consensus problems, Automatica, 46, 8, 1252-1265 (2010) · Zbl 1204.93013 |
| [20] | Munz, U.; Papachristodoulou, A.; Allgower, F., Robust consensus controller design for nonlinear relative degree two multi-agent systems with communication constraints, IEEE Transactions on Automatic Control, 56, 1, 145-151 (2011) · Zbl 1368.93224 |
| [21] | Munz, U.; Papachristodoulou, A.; Allgower, F., Consensus in multi-agent systems with coupling delays and switching topology, IEEE Transactions on Automatic Control, 56, 12, 2976-2982 (2011) · Zbl 1368.93010 |
| [22] | Munz, U.; Papachristodoulou, A.; Allgower, F., Delay robustness in non-identical multi-agent systems, IEEE Transactions on Automatic Control, 57, 6, 1597-1603 (2012) · Zbl 1369.93039 |
| [23] | Olfati-Saber, R.; Murray, R., 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 |
| [24] | Qin, J.; Gao, H.; Zheng, W. X., Second-order consensus for multi-agent systems with switching topology and communication delay, Systems & Control Letters, 60, 6, 390-397 (2011) · Zbl 1225.93020 |
| [25] | Ren, W.; Beard, R.; Atkins, E., Information consensus in multi-vehicle cooperative control, IEEE Control Systems Magazine, 27, 2, 71-82 (2007) |
| [26] | Ren, W.; Cao, Y., (Distributed coordination of multi-agent networks. Distributed coordination of multi-agent networks, Communications and control engineering series (2011), Springer-Verlag: Springer-Verlag London) · Zbl 1225.93003 |
| [28] | Rudy, C.; Olgac, N., An exact method for the stability analysis of linear consensus protocols with time delay, IEEE Transactions on Automatic Control, 56, 7, 1734-1740 (2011) · Zbl 1368.93591 |
| [29] | Seo, J. H.; Shim, H.; Back, J., Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach, Automatica, 45, 2659-2664 (2009) · Zbl 1180.93005 |
| [30] | Su, Y.; Huang, J., Stability of a class of linear switching systems with applications to two consensus problems, IEEE Transactions on Automatic Control, 57, 6, 1420-1430 (2012) · Zbl 1369.93387 |
| [31] | Su, Y.; Huang, J., Two consensus problems for discrete-time multi-agent systems with switching network topology, Automatica, 48, 9, 1988-1997 (2012) · Zbl 1258.93015 |
| [32] | Su, H.; Wang, X.; Chen, G., A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements, International Journal of Control, 83, 7, 1334-1343 (2009) · Zbl 1168.93311 |
| [33] | Su, H.; Wang, X.; Chen, G., Rendezvous of multiple mobile agents with preserved network connectivity, Systems & Control Letters, 59, 5, 313-322 (2010) · Zbl 1191.93005 |
| [34] | Tian, Y.; Liu, C., Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations, Automatica, 45, 1347-1353 (2009) · Zbl 1162.93027 |
| [35] | Tian, Y.; Zhang, Y., High-order consensus of heterogeneous multi-agent systems with unknown communication delays, Automatica, 48, 6, 1205-1212 (2012) · Zbl 1244.93013 |
| [36] | Wang, X.; Saberi, A.; Stoorvogel, A. A.; Grip, H. F.; Yang, T., Consensus in the network with uniform constant communication delay, Automatica, 49, 8, 2461-2467 (2013) · Zbl 1364.93034 |
| [37] | You, K.; Xie, L., Coordination of discrete-time multi-agent systems via relative output feedback, International Journal of Robust and Nonlinear Control, 21, 13, 1587-1605 (2011) · Zbl 1227.93013 |
| [38] | You, K.; Xie, L., Network topology and communication data rate for consensusability of discrete-time multi-agent systems, IEEE Transactions on Automatic Control, 56, 10, 2262-2275 (2011) · Zbl 1368.93014 |
| [39] | Yu, W.; Chen, G.; Cao, M., Distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities, Systems & Control Letters, 59, 9, 543-552 (2010) · Zbl 1207.37054 |
| [40] | Yu, W.; Chen, G.; Cao, M., Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems, Automatica, 46, 1089-1095 (2010) · Zbl 1192.93019 |
| [41] | Zhang, H.; Lewis, F. L., Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics, Automatica, 48, 1432-1439 (2012) · Zbl 1348.93144 |
| [42] | Zhang, H.; Lewis, F. L.; Das, A., Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback, IEEE Transactions on Automatic Control, 56, 8, 1948-1952 (2011) · Zbl 1368.93265 |
| [43] | Zhou, B.; Lin, Z.; Duan, G., Global and semi-global stabilization of linear systems with multiple delays and saturations in the input, SIAM Journal on Control and Optimization, 48, 8, 5294-5332 (2010) · Zbl 1218.34093 |
| [44] | Zhou, B.; Lin, Z.; Duan, G., \(L_\infty\) and \(L_2\) low gain feedback: their properties, characterizations and applications in constrained control, IEEE Transactions on Automatic Control, 56, 5, 1030-1045 (2011) · Zbl 1368.93235 |
| [45] | Zhou, B.; Lin, Z.; Duan, G., Truncated predictor feedback for linear systems with long time-varying input delays, Automatica, 48, 10, 2387-2399 (2012) · Zbl 1271.93123 |
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