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Sampled-data leader-following consensus of nonlinear multi-agent systems subject to impulsive perturbations. (English) Zbl 1476.93145

Summary: In this paper, the sampled-data leader-following consensus is investigated for a class of nonlinear multi-agent systems, where all agents are influenced by impulsive perturbations emerging from the input channels. Using the algebraic graph theory, the leader-following consensus problem of the multi-agent system is transformed into the stability problem of a constructed error system. By the Lyapunov functional method and the impulsive system theory, sufficient conditions for leader-following consensus of the underlying multi-agent systems are given. The proposed results are then extended to the containment control of multi-agent systems with multiple leaders. Finally, two numerical examples are presented to show the validity of the proposed results.

MSC:

93D50 Consensus
93A16 Multi-agent systems
93A13 Hierarchical systems
93C57 Sampled-data control/observation systems
93C10 Nonlinear systems in control theory
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[1] Häusle, A. J.; Saccon, A.; Aguiar, A. P.; Hause, J.; Pascoal, A. M., Energy-optimal motion planning for multiple robotic vehicles with collision avoidance, IEEE Trans Control Syst Technol, 24, 3, 867-883 (2016)
[2] Baldon, R.; Corsaro, A.; Querzoni, L.; Scipioni, S.; Piergiovanni, S. T., Coupling-based internal clock synchronization for large-scale dynamic distributed systems, IEEE Trans Parallel Distrib Syst, 21, 5, 607-619 (2010)
[3] Dong, X.; Yu, B.; Shi, Z.; Zhong, Y., Time-varying formation control for unmanned aerial vehicles: theories and applications, IEEE Trans Control Syst Technol, 23, 1, 340-348 (2015)
[4] Li, Y.; Lou, J.; Wang, Z.; Alsaad, F. E., Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers, J Franklin Inst, 355, 6520-6530 (2018) · Zbl 1398.93144
[5] Zhang, J.; Zhu, F., Observer-based output consensus of a class of heterogeneous multi-agent systems with unmatched disturbances, Commun Nonlinear Sci Numer Simul, 56, 240-251 (2018) · Zbl 1510.93036
[6] Wang, G.; Shen, Y., Second-order cluster consensus of multi-agent dynamical systems with impulsive effects, Commun Nonlinear Sci Numer Simul, 19, 9, 3220-3228 (2014) · Zbl 1510.93028
[7] Chen, S.; Ho, D. W.C.; Li, L.; Liu, M., Fault-tolerant consensus of multi-agent system with distributed adaptive protocol, IEEE Trans Cybern, 45, 10, 2142-2155 (2015)
[8] Lu, J.; Guo, X.; Huang, T.; Wang, Z., Consensus of signed networked multi-agent systems with nonlinear coupling and communication delays, Appl Math Comput, 350, 153-162 (2019) · Zbl 1428.93011
[9] Liu, L., Adaptive cooperative output regulation for a class of nonlinear multi-agent systems, IEEE Trans Autom Control, 60, 6, 1677-1682 (2015) · Zbl 1360.93357
[10] Hua, C.; Li, K.; Guan, X., Leader-following output consensus for high-order nonlinear multi-agent systems, IEEE Trans Autom Control, 64, 3, 1156-1161 (2019) · Zbl 1482.93038
[11] Wang, C.; Zuo, Z.; Qi, Z.; Ding, Z., Predictor-based extended-state-observer design for consensus of MASs with delay and disturbances, IEEE Trans Cybern, 49, 4, 1259-1269 (2019)
[12] Zou, W.; Xiang, Z.; Ahn, C., Mean square leader-following consensus of second-order nonlinear multi-agent systems with noises and unmodeled dynamics, IEEE Trans Syst Man Cybern Syst (2018)
[13] Yang, S.; Li, C.; Huang, T.; Zhang, W., Fixed-time consensus of complex dynamical networks with nonlinear coupling and fuzzy state-dependent uncertainties, Fuzzy Sets Syst (2018)
[14] Zou, W.; Ahn, C. K.; Xiang, Z., Leader-following consensus of second-order nonlinear multi-agent systems with unmodeled dynamics, Neurocomputing, 322, 120-129 (2018)
[15] Shen, D.; Xu, J., Distributed learning consensus for heterogenous high-order nonlinear multi-agent systems with output constraints, Automatica, 97, 64-72 (2018) · Zbl 1406.93031
[16] Khalili, M.; Zhang, X.; Polycarpou, M. M.; Parisini, T.; Cao, Y., Distributed adaptive fault-tolerant control of uncertain multi-agent systems, Automatica, 87, 142-151 (2018) · Zbl 1378.93040
[17] Liu, T.; Huang, J., A distributed observer for a class of nonlinear systems and its application to a leader-following consensus problem, IEEE Trans Autom Control, 64, 3, 1221-1227 (2019) · Zbl 1482.93021
[18] Lin, F., Performance of leader-follower multi-agent systems in directed networks, Syst Control Lett, 113, 52-58 (2018) · Zbl 1386.93011
[19] Hu, W.; Liu, L.; Feng, G., Event-triggered cooperative output regulation of linear multi-agent systems under jointly connected topologies, IEEE Trans Autom Control, 64, 3, 1317-1322 (2019) · Zbl 1482.93041
[20] Zou, W.; Xiang, Z., Event-triggered leader-following consensus of nonlinear multi-agent systems with switched dynamics, IET Control Theory Appl (2019) · Zbl 1432.93020
[21] Huang, N.; Duan, Z.; Chen, G., Some necessary and sufficient conditions for consensus of second-order multi-agent systems with sampled position data, Automatica, 63, 148-155 (2016) · Zbl 1329.93009
[22] Zhou, L.; Pan, Y.; Xiao, X., Synchronization of a class of switched nonlinear systems based on quantized sampled-data, Commun Nonlinear Sci Numer Simul, 70, 170-180 (2019) · Zbl 1464.93031
[23] Li, S.; Ahn, C.; Xiang, Z., Sampled-data adaptive output feedback fuzzy stabilization for switched nonlinear systems with asynchronous switching, IEEE Trans Fuzzy Syst, 27, 1, 200-205 (2018)
[24] Li, S.; Guo, J.; Xiang, Z., Global stabilization of a class of switched nonlinear systems under sampled-data control, IEEE Trans Syst Man Cybern Syst (2018)
[25] Liu, S.; Li, T.; Xie, L.; Fu, M.; Zhang, J., Continuous-time and sampled-data-based average consensus with logarithmic quantizers, Automatica, 49, 3329-3336 (2013) · Zbl 1315.93005
[26] Wu, Y.; Wang, L., Sampled-data consensus for multi-agent systems with quantised communication, Int J Control, 88, 2, 413-428 (2015) · Zbl 1328.93159
[27] Yu, Z.; Jiang, H.; Hu, C., Second-order consensus for multi-agent systems via intermittent sampled data control, IEEE Trans Syst Man Cybern Syst, 48, 11, 1986-2002 (2018)
[28] Shi, L.; Gu, H.; Yu, M.; Chen, B.; Xie, D., Consensus tracking control for sampled-data second-order multi-agent systems with arbitrary weights under fixed communication topology, Int J Syst Sci, 49, 9, 2025-2038 (2018) · Zbl 1481.93119
[29] Liu, K.; Mu, X.; Li, T., Sampled-data-based consensus of continuous-time systems with limited data rate, IET Control Theory Appl, 11, 14, 2328-2335 (2017)
[30] Zhang, W.; Tang, Y.; Huang, T.; Kurths, J., Sampled-data consensus of linear multi-agent systems with packet losses, IEEE Trans Neural NetwLearn Syst, 28, 11, 2516-2527 (2017)
[31] Li, X.; Chen, M. Z.Q.; Su, H., Quantized consensus of multi-agent networks with sampled data and Markovian interaction links, IEEE Trans Cybern, 49, 5, 1816-1825 (2019)
[32] Xing, M.; Deng, F.; Hu, Z., Sampled-data consensus for multi-agent systems with time delays and packet losses, IEEE Trans Syst Man Cybern Syst (2018)
[33] Zhang, W.; Wang, Z.; Liu, Y.; Ding, D.; Alsaadi, F. E., Sampled-data consensus of nonlinear multiagent systems subject to cyber attacks, Int J Robust Nonlinear Control, 28, 1, 53-67 (2018) · Zbl 1387.93028
[34] Zou, W.; Guo, G.; Xiang, Z., Sampled-data leader-following consensus of second-order nonlinear multiagent systems without velocity measurements, Int J Robust Nonlinear Control, 28, 17, 5634-5651 (2018) · Zbl 1408.93005
[35] Peng, C.; Zhang, J.; Han, Q., Consensus of multiagent systems with nonlinear dynamics using an integrated sampled-data-based event-triggered communication scheme, IEEE Trans Syst Man Cybern Syst, 65, 12, 4363-4375 (2018)
[36] Ding, L.; Zheng, W., Consensus tracking in heterogeneous nonlinear multi-agent networks with asynchronous sampled-data communication, Syst Control Lett, 96, 151-157 (2016) · Zbl 1347.93011
[37] Wen, G.; Duan, Z.; Yu, W.; Chen, G., Consensus of multi-agent systems with nonlinear dynamics and sampled-data information: a delayed-input approach, Int J Robust Nonlinear Control, 23, 6, 602-619 (2013) · Zbl 1273.93012
[38] He, W.; Zhang, B.; Han, Q.; Qian, F.; Jurths, J.; Cao, J., Leader-following consensus of nonlinear multiagent systems with stochastic sampling, IEEE Trans Cybern, 47, 2, 327-338 (2017)
[39] Zhao, X.; Zheng, X.; Ma, C.; Li, R., Distributed consensus of multiple euler-lagrange systems networked by sampled-data information with transmission delays and data packet dropouts, IEEE Trans Autom Sci Eng, 14, 3, 1440-1450 (2017)
[40] Li, X.; Shen, J.; Akca, H.; Rakkiyappan, R., Comparison principle for impulsive functional differential equations with infinite delays and applications, Commun Nonlinear Sci Numer Simul, 57, 309-321 (2018) · Zbl 1510.34146
[41] Yang, X.; Li, C.; Song, Q.; Li, H.; Huang, J., Effects of state-dependent impulses on robust exponential stability of quaternion-valued neural networks under parametric uncertainty, IEEE Trans Neural Netw Learn Syst (2018)
[42] Li, Y., Impulsive synchronization of stochastic neural networks via controlling partial states, Neural Process Lett, 46, 1, 59-69 (2017)
[43] He, W.; Gao, X.; Zhong, W.; Qian, F., Secure impulsive synchronization control of multi-agent systems under deception attacks, Inf Sci, 459, 354-368 (2018) · Zbl 1448.93248
[44] Xu, Z.; Li, C.; Han, Y., Leader-following fixed-time quantized consensus of multi-agent systems via impulsive control, J Franklin Inst, 356, 1, 441-456 (2019) · Zbl 1405.93010
[45] Guan, Z.; Hu, B.; Chi, M.; He, D.; Cheng, X., Guaranteed performance consensus in second-order multi-agent systems with hybrid impulsive control, Automatica, 50, 2415-2418 (2014) · Zbl 1297.93012
[46] Chen, L.; Sun, J., Distributed optimal control and \(l_2\) gain performance for the multi-agent system with impulsive effects, Syst Control Lett, 113, 65-70 (2018) · Zbl 1386.93004
[47] Wang, G.; Shen, Y., Second-order cluster consensus of multi-agent dynamical systems with impulsive effects, Commun Nonlinear Sci Numer Simul, 19, 3220-3228 (2014) · Zbl 1510.93028
[48] Ma, T.; Lewis, F. L.; Song, Y., Exponential synchronization of nonlinear multi-agent systems with time delays and impulsive disturbances, Int J Robust Nonlinear Control, 26, 8, 1615-1631 (2016) · Zbl 1342.93011
[49] Meng, Z.; Ren, W.; You, Z., Distributed finite-time attitude containment control for multiple rigid bodies, Automatica, 46, 12, 2092-2099 (2010) · Zbl 1205.93010
[50] Hardy, G. H.; Littlewood, J. E.; Polya, G. (1952), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0047.05302
[51] Apostol, T., Mathematical analysis (1974), Addison-Wesley: Addison-Wesley New Jersey · Zbl 0309.26002
[52] Michel, A. N.; Miller, R. K., Qualitative analysis of large scale dynamical systems (1977), Academic Press: Academic Press New York · Zbl 0494.93002
[53] Wang, Q.; Fu, J.; Wang, J., Fully distributed containment control of high-order multi-agent systems with nonlinear dynamics, Syst Control Lett, 99, 33-39 (2017) · Zbl 1353.93010
[54] Zhang, Y.; Yang, Y., Finite-time consensus of second-order leader-following multi-agent systems without velocity measurements, Physics A, 377, 3-4, 243-249 (2013) · Zbl 1298.91116
[55] Li, X.; Ho, D. W.C.; Cao, J., Finite-time stability and settling-time estimation of nonlinear impulsive systems, Automatica, 99, 361-368 (2019) · Zbl 1406.93260
[56] Xia, J.; Zhang, J.; Zhang, B.; Wang, Z., Finite-time adaptive fuzzy control for nonlinear systems with full state constraints, IEEE Trans Syst Man Cybern Syst (2018)
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