×

\(\mathcal H_\infty \) consensus control for multi-agent systems with missing measurements: the finite-horizon case. (English) Zbl 1281.93010

Summary: This paper deals with the \(\mathcal H_\infty \) consensus control problem for a class of discrete time-varying multi-agent systems with both missing measurements and parameter uncertainties. A directed graph is used to represent the communication topology of the multi-agent network, and a binary switching sequence satisfying a conditional probability distribution is employed to describe the missing measurements. The purpose of the addressed problem is to design a time-varying controller such that, for all probabilistic missing observations and admissible parameter uncertainties, the \(\mathcal H_\infty \) consensus performance is guaranteed over a given finite horizon for the closed-loop networked multi-agent systems. According to the given topology, the measurement output available for the controller is not only from the individual agent but also from its neighboring agents. By using the completing squares method and stochastic analysis techniques, necessary and sufficient conditions are derived for the \(\mathcal H_\infty \) consensus to be ensured. The parameters of the time-varying controller are designed by solving coupled backward recursive Riccati Difference Equations (RDEs). A simulation example is utilized to illustrate the usefulness of the proposed control protocol.

MSC:

93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93B36 \(H^\infty\)-control
PDFBibTeX XMLCite
Full Text: DOI

References:

[2] 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
[3] 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
[4] Abdollahi, F.; Khorasani, K., A decentralized Markovian jump \(H_\infty\) control routing strategy for mobile multi-agent networked systems, IEEE Transactions on Control Systems Technology, 19, 2, 269-283 (2011)
[5] Olfati-Saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE Transactions on Automatic Control, 51, 3, 401-420 (2006) · Zbl 1366.93391
[6] 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
[7] 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
[8] Yang, P.; Freeman, R.; Lynch, K., Multi-agent coordination by decentralized estimation and control, IEEE Transactions on Automatic Control, 53, 11, 2480-2496 (2008) · Zbl 1367.93040
[9] Yu, W.; Chen, G.; Wang, Z.; Yang, W., Distributed consensus filtering in sensor networks, IEEE Transactions on Systems, Man, and Cybernetics—Part B, 39, 6, 1568-1577 (2009)
[10] Kar, S.; Moura, J. M.F., Distributed consensus algorithms in sensor networks: quantized data and random link failures, IEEE Transactions on Signal Processing, 58, 3, 1383-1399 (2010) · Zbl 1392.94269
[11] Shen, B.; Wang, Z.; Hung, Y. S., 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
[12] Sorrentino, F.; Di Bernardo, M.; Garofalo, F., Synchronizability and synchronization dynamics of weighed and unweighed scale free networks with degree mixing, International Journal of Bifurcation and Chaos, 17, 7, 2419-2434 (2007) · Zbl 1144.82352
[13] Shen, B.; Wang, Z.; Liu, X., Bounded \(H_\infty\) synchronization and state estimation for discrete time-varying stochastic complex networks over a finite horizon, IEEE Transactions on Neural Networks, 22, 1, 145-157 (2011)
[14] Ma, C.; Zhang, J., Necessary and sufficient conditions for consensusability of linear multi-agent systems, IEEE Transactions on Automatic Control, 55, 5, 1263-1268 (2010) · Zbl 1368.93383
[15] Li, T.; Fu, M.; Xie, L.; Zhang, J., Distributed consensus with limited communication data rate, IEEE Transactions on Automatic Control, 56, 2, 279-292 (2011) · Zbl 1368.93346
[16] 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
[17] Huang, M.; Manton, J. H., Stochastic consensus seeking with noisy and directed inter-agent communication: fixed and randomly varying topologies, IEEE Transactions on Automatic Control, 55, 1, 235-241 (2010) · Zbl 1368.94002
[18] Ma, H., Decentralized adaptive synchronization of a stochastic discrete-time multiagent dynamic model, SIAM Journal on Control and Optimization, 48, 2, 859-880 (2009) · Zbl 1194.93104
[19] Patterson, S.; Bamieh, B.; Abbadi, A., Convergence rates of distributed average consensus with stochastic link failures, IEEE Transactions on Automatic Control, 55, 4, 880-892 (2010) · Zbl 1368.94198
[20] Gu, D., A game theory approach to target tracking in sensor networks, IEEE Transactions on Systems, Man, and Cybernetics—Part B, 41, 1, 2-13 (2011)
[21] Semsar-Kazerooni, E.; Khorasani, K., Multi-agent team cooperation: a game theory approach, Automatica, 45, 10, 2205-2213 (2009) · Zbl 1179.93025
[22] 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, 988-1000 (2003) · Zbl 1364.93514
[23] Olfati-Saber, R.; Fax, J. A.; Murray, R. M., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 1, 215-233 (2007) · Zbl 1376.68138
[24] 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
[25] Ren, W., On consensus algorithms for double-integrator dynamics, IEEE Transactions on Automatic Control, 58, 6, 1503-1509 (2008) · Zbl 1367.93567
[26] Qin, J.; Zheng, W. X.; Gao, H., Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology, Automatica, 47, 9, 1983-1991 (2011) · Zbl 1227.93011
[27] Liu, Y.; Jia, Y., Consensus problem of high-order multi-agent systems with external disturbances: an \(H_\infty\) analysis approach, International Journal of Robust and Nonlinear Control, 20, 14, 1579-1593 (2010) · Zbl 1204.93043
[28] Hermoso-Carazo, A.; Jimenez-Lopez, J. D.; Linares-Perez, J., Recursive smoothing algorithms for the estimation of signals from uncertain observations via mixture approximations, International Journal of Systems Science, 41, 6, 647-656 (2010) · Zbl 1193.93163
[29] Basin, M.; Shi, P.; Calderon-Alvarez, D., Joint state filtering and parameter estimation for linear stochastic time-delay systems, Signal Processing, 91, 4, 782-792 (2011) · Zbl 1217.94034
[30] Elmadssia, S.; Saadaoui, K.; Benrejeb, M., New delay-dependent stability conditions for linear systems with delay, Systems Science & Control Engineering: An Open Access Journal, 1, 2-11 (2013)
[31] Chen, Y.; Hoo, K. A., Stability analysis for closed-loop management of a reservoir based on identification of reduced-order nonlinear model, Systems Science & Control Engineering: An Open Access Journal, 1, 12-19 (2013)
[32] Li, Z.; Duan, Z.; Chen, G., On \(H_\infty\) and \(H_2\) performance regions of multi-agent systems, Automatica, 47, 4, 797-803 (2011) · Zbl 1215.93042
[33] Aeyels, D.; De Smet, F., Cluster formation in a time-varying multi-agent system, Automatica, 47, 11, 2481-2487 (2011) · Zbl 1228.93007
[34] 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
[35] Sun, Y.; Guan, Z.; Zhan, X.; Yuan, F., Consensus of second-order and high-order discrete-time multi-agent systems with random networks, Nonlinear Analysis. Real World Applications, 13, 5, 1979-1990 (2012) · Zbl 1254.93011
[36] Hung, Y. S.; Yang, F., Robust \(H_\infty\) filtering for discrete time-varying uncertain systems with a known deterministic input, International Journal of Control, 75, 15, 1159-1169 (2002) · Zbl 1146.93378
[37] Ding, D.; Wang, Z.; Dong, H.; Shu, H., Distributed \(H_\infty\) state estimation with stochastic parameters and nonlinearities through sensor networks: the finite-horizon case, Automatica, 48, 8, 1575-1585 (2012) · Zbl 1267.93167
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.