# zbMATH — the first resource for mathematics

Output regulation for heterogeneous linear multi-agent systems based on distributed internal model compensator. (English) Zbl 1334.93014
Summary: This article considers robust output regulation of uncertain heterogeneous multi-agent systems in the case that all the agents have non-identical nominal dynamics. The directed communication graph contains a spanning tree and the exosystem is as its root. Since not all the agents can access the information of the exosystem, the distributed compensator is used for the unaccessible part. The dynamic state feedback control law and dynamic output feedback control law are proposed under this topological structure. Then we give a novel compact form and a general global method to solve the robust output regulation problem based on internal model principle. Finally, some examples are presented to illustrate the effectiveness of our results.

##### MSC:
 93A14 Decentralized systems 93D15 Stabilization of systems by feedback 93C05 Linear systems in control theory
Full Text:
##### References:
 [1] Jadbabaie, A.; Lin, J.; Morse, A., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Autom. Control, 48, 988-1001, (2003) · Zbl 1364.93514 [2] Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Autom. Control, 49, 1520-1533, (2004) · Zbl 1365.93301 [3] R. Olfati-Saber, J.A. Fax, R.M. Murray, Consensus and cooperation in networked multi-agent systems, in: Proceedings of the IEEE, vol. 95, 2007, pp. 215-223. · Zbl 1376.68138 [4] Pietro, D.; Mario, D.; Franco, G.; Davide, L., Analysis and stability of consensus in networked control systems, Appl. Math. Comput., 217, 988-1000, (2010) · Zbl 1207.93007 [5] Liu, Y. R.; Daniel, W. C.H.; Wang, Z. D., A new framework for consensus for discrete-time directed networks of multi-agents with distributed delays, Int. J. Control, 85, 1755-1765, (2012) · Zbl 1253.93081 [6] Liu, B.; Su, H. S.; Li, R.; Sun, D. H.; Hu, W. N., Switching controllability of discrete-time multi-agent systems with multiple leaders and time-delays, Appl. Math. Comput., 228, 571-588, (2014) · Zbl 1364.93069 [7] Zhao, H. Y.; Park, J. H.; Zhang, Y. L., Couple-group consensus for second-order multi-agent systems with fixed and stochastic switching topologies, Appl. Math. Comput., 232, 595-605, (2014) · Zbl 1410.93016 [8] Q. Ma, S.Y. Xu, F.L. Lewis, Second-order consensus for directed multi-agent systems with sampled data, Int. J. Robust Nonlinear Control. 2013. http://dx.doi.org/10.1002/rnc.3010, in press. · Zbl 1302.93009 [9] Q. Ma, F.L. Lewis, S.Y. Xu, Cooperative containment of discrete-time linear multi-agent systems, Int. J. Robust Nonlinear Control. 2013. http://dx.doi.org/10.1002/rnc.3124, in press. · Zbl 1312.93007 [10] Yang, H.; Jiang, B.; Cocquempot, V.; Zhang, H. G., Stabilization of switched nonlinear systems with all unstable modes: applications to multi-agent systems, IEEE Trans. Autom. Control, 56, 2230-2235, (2011) · Zbl 1368.93580 [11] Yang, H.; Jiang, B.; Zhang, H. G., Stabilization of non-minimum phase switched nonlinear systems with application to multi-agent systems, Syst. Control Lett., 61, 1023-1031, (2012) · Zbl 1270.93083 [12] Zhang, H. G.; Liu, D. R.; Luo, Y. H.; Wang, D., Adaptive dynamic programming for control-algorithms and stability, (2013), Springer-Verlag London [13] Ma, Q.; Wang, Z.; Miao, G. Y., Second-order group consensus for multi-agent systems via pinning leader-following approach, J. Franklin Inst., 351, 1288-1300, (2014) · Zbl 1395.93020 [14] Hong, Y. G.; Hu, J. P.; Gao, L. X., Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 42, 1177-1182, (2006) · Zbl 1117.93300 [15] Y. Zhao, Z.K. Li, Z.S. Duan, Distributed consensus tracking of multi-agent systems with nonlinear dynamics under a reference leader, Int. J. Control. http://dx.doi.org/10.1080/00207179.2013.797608. · Zbl 1311.93005 [16] Francis, B. A., The linear multivariable regulator problem, SIAM J. Control Optim., 15, 486-505, (1977) · Zbl 0382.93025 [17] Isidori, A.; Byrnes, C., Output regulation of nonlinear systems, IEEE Trans. Autom. Control, 35, 131-140, (1990) · Zbl 0704.93034 [18] Li, R. R.; Khalil, H., Nonlinear output regulation with adaptive conditional servocompensator, Automatica, 48, 2550-2559, (2012) · Zbl 1271.93089 [19] Xiang, J.; Wei, W.; Li, Y., Synchronized output regulation of networked linear systems, IEEE Trans. Autom. Control, 54, 1336-1341, (2009) · Zbl 1367.93450 [20] Su, Y. F.; Huang, J., Cooperative output regulation of linear multi-agent systems, IEEE Trans. Autom. Control, 57, 1062-1066, (2012) · Zbl 1369.93051 [21] Huang, C.; Ye, X.; Sun, Z., Output regulation problem of multi-agents in networked systems, IET Control Theory Appl., 6, 971-978, (2012) [22] Wang, X. L.; Hong, Y. G.; Huang, J.; Jiang, Z. P., A distributed control approach to a robust output regulation problem for multi-agent linear systems, IEEE Trans. Autom. Control, 55, 2891-2895, (2010) · Zbl 1368.93577 [23] Wang, X. L.; Han, F., Robust coordination control of switching multi-agent systems via output regulation approach, Kybernetika, 47, 755-772, (2011) · Zbl 1236.93010 [24] Wieland, P.; Sepulchre, R.; Allgwer, F., An internal model principle is necessary and sufficient for linear output synchronization, Automatica, 47, 1068-1074, (2011) · Zbl 1233.93011 [25] Yu, L.; Wang, J. Z., Robust cooperative control for multi-agent systems via distributed output regulation, Syst. Control Lett., 62, 1049-1056, (2013) · Zbl 1281.93014 [26] Liang, H. J.; Zhang, H. G.; Wang, Z. S.; Wang, J., Output regulation of state-coupled linear multi-agent systems with globally reachable topologies, Neurocomputing, 123, 337-343, (2014) [27] Su, Y. F.; Hong, Y. G.; Huang, J., A general result on the robust cooperative output regulation for linear uncertain multi-agent systems, IEEE Trans. Autom. Control, 58, 1275-1279, (2013) · Zbl 1369.93050 [28] Godsil, C.; Royle, G., Algebraic graph theory, (2001), Springer-Verlag New York · Zbl 0968.05002 [29] Jan, L., Synchronization of heterogeneous agents, IEEE Trans. Autom. Control, 57, 2885-2890, (2012) · Zbl 1369.93037 [30] Li, Z. K.; Duan, Z. S.; Chen, G. R.; Huang, L., Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint, IEEE Trans. Circuits Syst., I, 57, 213-224, (2010) [31] Huang, J., Nonlinear output regulation: theory and applications, (2004), SIAM Phildelphia, PA · Zbl 1087.93003 [32] Su, Y. F.; Huang, J., Cooperative output regulation of linear multi-agent systems by output feedback, Syst. Control Lett., 61, 1248-1253, (2012) · Zbl 1255.93014
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.