Robust consensus tracking of a class of second-order multi-agent dynamic systems. (English) Zbl 1250.93009

Summary: In this paper, we study the problem of robust consensus tracking for a class of second-order multi-agent dynamic systems with disturbances and unmodeled agent dynamics. Contrary to previous approaches, we design continuous distributed consensus protocols to enable global asymptotic consensus tracking. Our focus is on consensus protocol design and stability analysis which also leads to the derivation of sufficient conditions for consensus tracking. We first consider the case of undirected information exchange with a symmetric and positive definite information-exchange matrix. We develop an identifier for each agent to estimate the unknown disturbances and unmodeled agent dynamics. Based on the identifier, we develop a consensus tracking protocol to enable global asymptotic consensus tracking using local information obtained from neighboring agents. The closed-loop stability is proven using Lyapunov analysis theory and an invariance-like theorem. We then extend the approach to the case of directed information exchange, whose information-exchange matrix is only of full rank so that the approach for undirected graphs cannot be directly applied. We show that global asymptotic consensus tracking can still be enabled under the new derived sufficient conditions by designing a new identifier, which utilizes the estimated information exchanged from neighboring agents, and constructing a new Lyapunov function. Examples and numerical simulations are provided to validate the effectiveness of the proposed robust consensus tracking method.


93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
Full Text: DOI


[1] Olfati-Saber, R.; Fax, J.A.; Murray, R.M., Consensus and cooperation in networked multi-agent systems, Proc. IEEE, 95, 1, 215-233, (2007) · Zbl 1376.68138
[2] Ren, W.; Beard, R.W.; Atkins, E., Information consensus in multivehicle cooperative control: collective group behavior through local interaction, IEEE control syst. mag., 27, 2, 71-82, (2007)
[3] 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
[4] 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
[5] Fax, A.; Murray, R.M., Information flow and cooperative control of vehicle formations, IEEE trans. automat. control, 49, 9, 1465-1476, (2004) · Zbl 1365.90056
[6] 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
[7] Moreau, L., Stability of multi-agent systems with time-dependent communication links, IEEE trans. automat. control, 50, 2, 169-182, (2005) · Zbl 1365.93268
[8] Olfati-Saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE trans. automat. control, 51, 3, 401-420, (2006) · Zbl 1366.93391
[9] 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
[10] Xie, G.; Wang, L., Consensus control for a class of networks of dynamic agents, Int. J. robust nonlinear control, 17, 10-11, 941-959, (2007) · Zbl 1266.93013
[11] Sarlette, A.; Sepulchre, R.; Leonard, N., Autonomous rigid body attitude synchronization, Automatica, 45, 2, 572-577, (2009) · Zbl 1158.93372
[12] Ren, W., Distributed cooperative attitude synchronization and tracking for multiple rigid bodies, IEEE trans. control syst. technol., 18, 2, 383-392, (2010)
[13] 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
[14] Lafferriere, G.; Williams, A.; Caughman, J.; Veerman, J.J.P., Decentralized control of vehicle formations, Systems control lett., 54, 9, 899-910, (2005) · Zbl 1129.93303
[15] Porfiri, M.; Roberson, D.; Stilwell, D., Tracking and formation control of multiple autonomous agents: A two-level consensus approach, Automatica, 43, 8, 1318-1328, (2007) · Zbl 1130.93349
[16] Anderson, B.; Yu, C.; Fidan, B.; Hendrickx, J., Rigid graph control architectures for autonomous formations, IEEE control syst. mag., 28, 6, 48-63, (2008) · Zbl 1395.93383
[17] Lee, D.; Spong, M.W., Stable flocking of multiple inertial agents on balanced graphs, IEEE trans. automat. control, 52, 8, 1469-1475, (2007) · Zbl 1366.93503
[18] Tanner, H.G.; Jadbabaie, A.; Pappas, G.J., Flocking in fixed and switching networks, IEEE trans. automat. control, 52, 5, 863-868, (2007) · Zbl 1366.93414
[19] Su, H.; Wang, X.; Lin, Z., Flocking of multi-agents with a virtual leader, IEEE trans. automat. control, 54, 2, 293-307, (2009) · Zbl 1367.37059
[20] Lin, Z.; Broucke, M.; Francis, B., Local control strategies for groups of mobile autonomous agents, IEEE trans. automat. control, 49, 4, 622-629, (2004) · Zbl 1365.93208
[21] Ren, W.; Atkins, E.M., Distributed multi-vehicle coordinated control via local information exchange, Int. J. robust nonlinear control, 17, 10-11, 1002-1033, (2007) · Zbl 1266.93010
[22] Freeman, R.; Yang, P.; Lynch, K., Stability and convergence properties of dynamic average consensus estimators, Proc. IEEE conf. decision control, 398-403, (2006)
[23] Zhu, M.; Martinez, S., Discrete-time dynamic average consensus, Automatica, 46, 2, 322-329, (2010) · Zbl 1205.93014
[24] 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
[25] Feng, X.; Wang, L., Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE trans. automat. control, 53, 8, 1804-1816, (2008) · Zbl 1367.93255
[26] Xiao, F.; Wang, L., State consensus for multi-agent systems with switching topologies and time-varying delays, Int. J. control, 79, 10, 1277-1284, (2006) · Zbl 1330.94022
[27] Ren, W., Consensus tracking under directed interaction topologies: algorithms and experiments, IEEE trans. control syst. technol., 18, 1, 230-237, (2010)
[28] Khoo, S.; Xie, L.; Man, Z., Robust finite-time consensus tracking algorithm for multi-robot systems, IEEE/ASME trans. mechatron., 14, 2, 219-228, (2009)
[29] Hong, Y.; Chen, G.; Bushnell, L., Distributed observers design for leader following control of multi-agent networks, Automatica, 44, 3, 846-850, (2008) · Zbl 1283.93019
[30] Cao, Y.; Ren, W.; Meng, Z., Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking, Systems control lett., 59, 9, 522-529, (2010) · Zbl 1207.93103
[31] Y. Cao, W. Ren, Distributed coordinated tracking with reduced interaction via a variable structure approach, IEEE Trans. Automat. Control 56 (12) (2011) (in press). · Zbl 1369.93012
[32] Hu, G., Robust consensus tracking for an integrator-type multi-agent system with disturbances and unmodelled dynamics, Int. J. control, 84, 1, 1-8, (2011) · Zbl 1221.93012
[33] Hu, G., Robust consensus tracking of a class of second-order multi-agent dynamic systems, Proc. IEEE conf. decision control, 3214-3220, (2010)
[34] Khalil, H.K., Nonlinear systems, (2002), Prentice-Hall, Inc. New Jersey · Zbl 0626.34052
[35] Diestel, R., Graph theory, Graduate texts in mathematics, vol. 173, (1997), Springer-Verlag New York
[36] Merris, R., Laplacian matrices of graphs: a survey, Linear algebra appl., 197-198, 143-176, (1994) · Zbl 0802.05053
[37] Qu, Z., Cooperative control of dynamical systems: applications to autonomous vehicles, (2009), Springer · Zbl 1171.93005
[38] Hu, G.; Aiken, D.; Gupta, S.; Dixon, W.E., Lyapunov-based range identification for paracatadioptric systems, IEEE trans. automat. control, 53, 7, 1775-1781, (2008) · Zbl 1367.93091
[39] Makkar, C.; Hu, G.; Sawyer, W.G.; Dixon, W.E., Lyapunov-based tracking control in the presence of uncertain nonlinear parameterizable friction, IEEE trans. automat. control, 52, 10, 1988-1994, (2007) · Zbl 1366.93443
[40] Hardy, G.H.; Littlewood, J.E.; Polya, G., Inequalities, (1988), Cambridge University Press Cambridge, England · Zbl 0634.26008
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.