×

Distributed consensus tracking control of second-order non-linear multi-agent systems with unmodelled dynamics. (English) Zbl 07916957

Summary: In this study, the consensus tracking control problem is considered for a class of second-order non-linear multi-agent systems with unmodelled dynamics. Radial basis function neural networks are introduced to approximate the unknown non-linearities and a dynamic signal is utilised to deal with the unmodelled dynamics. Meanwhile, appropriate Lyapunov functions are constructed and a new distributed adaptive control protocol is designed to guarantee that all the tracking error signals in the considered multi-agent systems are ultimately bounded, under which the distributed tracking consensus is reached for all undirected connected communication graphs. Finally, two demonstrative examples are given to illustrate the validity of the designed protocols.
© 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons, Ltd. on behalf of The Institution of Engineering and Technology

MSC:

93D50 Consensus
93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
93A16 Multi-agent systems
93B70 Networked control
Full Text: DOI

References:

[1] SongQ.CaoJ.YuW.: ‘Second‐order leader‐following consensus of nonlinear multi‐agent systems via pinning control’, Syst. Control Lett., 2010, 59, (9), pp. 553-562 · Zbl 1213.37131
[2] JinX.WangS.QinJ. et al.: ‘Adaptive fault‐tolerant consensus for a class of uncertain nonlinear second‐order multi‐agent systems with circuit implementation’, IEEE Trans. Circuits Syst. I: Regul. Pap., 2017, 65, (7), pp. 2243-2255 · Zbl 1468.93096
[3] QinJ.ZhangG.ZhengW.X. et al.: ‘Adaptive sliding mode consensus tracking for second‐order nonlinear multiagent systems with actuator faults’, IEEE Trans. Cybern., 2018, 49, (5), pp. 1605-1615
[4] ChenC.L.P.RenC.E.DuT.: ‘Fuzzy observed‐based adaptive consensus tracking control for second‐order multiagent systems with heterogeneous nonlinear dynamics’, IEEE Trans. Fuzzy Syst., 2015, 24, (4), pp. 906-915
[5] WenG.ChenC.L.P.LiuY.J. et al.: ‘Neural network‐based adaptive leader‐following consensus control for a class of nonlinear multiagent state‐delay systems’, IEEE Trans. Cybern., 2017, 47, (8), pp. 2151-2160
[6] DingD.WangZ.HoD.W.C. et al.: ‘Observer‐based event‐triggering consensus control for multiagent systems with lossy sensors and cyber‐attacks’, IEEE Trans. Cybern., 2017, 47, (8), pp. 1936-1947
[7] DengC.YangG.H.: ‘Leaderless and leader‐following consensus of linear multi‐agent systems with distributed event‐triggered estimators’, J. Franklin Inst., 2019, 356, (1), pp. 309-333 · Zbl 1405.93009
[8] ZouW.XiangZ.: ‘Event‐triggered leader‐following consensus of nonlinear multi‐agent systems with switched dynamics’, IET Control Theory Applic., 2019, 13, (9), pp. 1222-1228 · Zbl 1432.93020
[9] HuangN.DuanZ.ZhaoY.: ‘Leader‐following consensus of second‐order non‐linear multi‐agent systems with directed intermittent communication’, IET Control Theory Applic., 2014, 8, (10), pp. 782-795
[10] WeiC.LuoJ.YinZ. et al.: ‘Leader‐following consensus of second‐order multi‐agent systems with arbitrarily appointed‐time prescribed performance’, IET Control Theory Applic., 2018, 12, (16), pp. 2276-2286
[11] ZhaoW.YuW.ZhangH.: ‘Observer‐based formation tracking control for leader‐follower multi‐agent systems’, IET Control Theory Applic., 2019, 13, (2), pp. 239-247 · Zbl 1434.93009
[12] ZhangL.ZhangZ.LawranceN. et al.: ‘Decentralised finite‐time consensus for second‐order multi‐agent system under event‐triggered strategy’, IET Control Theory Appl., 2020, 14, (4), pp. 664-673 · Zbl 07907137
[13] ZhaoY.LiuY.WenG. et al.: ‘Distributed finite‐time tracking of second‐order multi‐agent systems: an edge‐based approach’, IET Control Theory Applic., 2018, 12, (1), pp. 149-154
[14] WangJ.WuH.: ‘Leader‐following formation control of multi‐agent systems under fixed and switching topologies’, Int. J. Control, 2012, 85, (6), pp. 695-705 · Zbl 1256.93013
[15] MeiJ.RenW.MaG.: ‘Distributed coordination for second‐order multi‐agent systems with nonlinear dynamics using only relative position measurements’, Automatica, 2013, 49, (5), pp. 1419-1427 · Zbl 1319.93008
[16] LiH.LiaoX.HuangT.: ‘Second‐order locally dynamical consensus of multiagent systems with arbitrarily fast switching directed topologies’, IEEE Trans. Syst., Man, Cybern., Syst., 2013, 43, (6), pp. 1343-1353
[17] YuW.ChenG.CaoM. et al.: ‘Second‐order consensus for multiagent systems with directed topologies and nonlinear dynamics’, IEEE Trans. Syst., Man, Cybern. B, 2010, 40, (3), pp. 881-891
[18] HuaC.YouX.GuanX.: ‘Adaptive leader‐following consensus for second‐order time‐varying nonlinear multiagent systems’, IEEE Trans. Cybern., 2016, 47, (6), pp. 1532-1539
[19] DuH.HeY.ChengY.: ‘Finite‐time synchronization of a class of second‐order nonlinear multi‐agent systems using output feedback control’, IEEE Trans. Circuits Syst., 2014, 61, (6), pp. 1778-1788
[20] ZhaoY.LiuY.WenG. et al.: ‘Distributed average tracking for lipschitz‐type of nonlinear dynamical systems’, IEEE Trans. Cybern., 2019, 49, (12), pp. 4140-4152
[21] ZouW.AhnC.K.XiangZ.: ‘Leader‐following consensus of second‐order nonlinear multi‐agent systems with unmodeled dynamics’, Neurocomputing, 2018, 322, pp. 120-129
[22] TongS.LiY.ShiP.: ‘Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties’, Inf. Sci., 2009, 179, (9), pp. 1319-1332 · Zbl 1156.93357
[23] WangH.LiuW.QiuJ. et al.: ‘Adaptive fuzzy decentralized control for a class of strong interconnected nonlinear systems with unmodeled dynamics’, IEEE Trans. Fuzzy Syst., 2017, 26, (2), pp. 836-846
[24] ZhouQ.LiH.WuC. et al.: ‘Adaptive fuzzy control of nonlinear systems with unmodeled dynamics and input saturation using small‐gain approach’, IEEE Trans. Syst., Man, Cybern., Syst., 2016, 47, (8), pp. 1979-1989
[25] LiS.AhnC.K.XiangZ.: ‘Adaptive fuzzy control of switched nonlinear time‐varying delay systems with prescribed performance and unmodeled dynamics’, Fuzzy Set. Syst., 2019, 371, pp. 40-60 · Zbl 1423.93198
[26] YinS.YangH.GaoH. et al.: ‘An adaptive NN‐based approach for fault‐tolerant control of nonlinear time‐varying delay systems with unmodeled dynamics’, IEEE Trans. Neural Netw. Learn. Syst., 2016, 28, (8), pp. 1902-1913
[27] WangH.LiuP.X.LiS. et al.: ‘Adaptive neural output‐feedback control for a class of nonlower triangular nonlinear systems with unmodeled dynamics’, IEEE Trans. Neural Netw. Learn. Syst., 2017, 29, (8), pp. 3658-3668
[28] WangD.MaH.LiuD.: ‘Distributed control algorithm for bipartite consensus of the nonlinear time‐delayed multi‐agent systems with neural networks’, Neurocomputing, 2016, 174, pp. 928-936
[29] LiuY.: ‘Robust adaptive observer for nonlinear systems with unmodeled dynamics’, Automatica, 2009, 45, (8), pp. 1891-1895 · Zbl 1185.93021
[30] LiuY.LiX.Y.: ‘Decentralized robust adaptive control of nonlinear systems with unmodeled dynamics’, IEEE Trans. Autom. Control, 2002, 47, (5), pp. 848-856 · Zbl 1364.93401
[31] BhowmickS.PanjaS.: ‘Leader‐follower bipartite consensus of uncertain linear multiagent systems with external bounded disturbances over signed directed graph’, IEEE Control Syst. Lett., 2019, 3, (3), pp. 595-600
[32] JiangZ.P.PralyL.: ‘Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties’, Automatica, 1998, 34, (7), pp. 825-840 · Zbl 0951.93042
[33] HuJ.LinY.S.: ‘Consensus control for multi‐agent systems with double‐integrator dynamics and time delays’, IET Control Theory Applic., 2010, 4, (1), pp. 109-118
[34] ZhaoY.LiuY.WenG. et al.: ‘Designing distributed specified‐time consensus protocols for linear multiagent systems over directed graphs’, IEEE Trans. Autom. Control, 2019, 64, (7), pp. 2945-2952 · Zbl 1482.93065
[35] LiH.LiaoX.HuangT. et al.: ‘Event‐triggering sampling based leader‐following consensus in second‐order multi‐agent systems’, IEEE Trans. Autom. Control, 2015, 60, (7), pp. 1998-2003 · Zbl 1360.93031
[36] ZhaoY.NiuB.WangH. et al.: ‘Adaptive neural tracking control of nonlinear nonstrict‐feedback systems with unmodeled dynamics’, IEEE Access, 2019, 7, pp. 90206-90214
[37] HardyG.H.LittlewoodJ.E.PolyaG.: ‘Inequalities’ (Cambridge University Press, UK, 1952, 2nd edn.) · Zbl 0047.05302
[38] GeS.S.TeeK.P.: ‘Approximation‐based control of nonlinear MIMO time‐delay systems’, Automatica, 2007, 43, (1), pp. 31-43 · Zbl 1137.93042
[39] JinX.: ‘Adaptive iterative learning control for high‐order nonlinear multi‐agent systems consensus tracking’, Syst. Control Lett., 2016, 89, pp. 16-23 · Zbl 1335.93067
[40] ZhouB.LinZ.: ‘Consensus of high‐order multi‐agent systems with large input and communication delays’, Automatica, 2014, 50, (2), pp. 452-464 · Zbl 1364.93044
[41] ShiG.HongY.: ‘Global target aggregation and state agreement of nonlinear multi‐agent systems with switching topologies’, Automatica, 2009, 45, (5), pp. 1165-1175 · Zbl 1162.93308
[42] ZhangY.TianY.P.: ‘Consensus of data‐sampled multi‐agent systems with random communication delay and packet loss’, IEEE Trans. Autom. Control, 2010, 55, (4), pp. 939-943 · Zbl 1368.94067
[43] QinJ.GaoH.ZhengW.X.: ‘Second‐order consensus for multi‐agent systems with switching topology and communication delay’, Syst. Control Lett., 2011, 60, (6), pp. 390-397 · Zbl 1225.93020
[44] HuangJ.WenC.WangW.: ‘Adaptive finite‐time consensus control of a group of uncertain nonlinear mechanical systems’, Automatica, 2015, 51, pp. 292-301 · Zbl 1309.93011
[45] ZhaoY.LiuY.WenG. et al.: ‘Edge‐based finite‐time protocol analysis with final consensus value and settling time estimations’, IEEE Trans. Cybern., 2020, 50, (4), pp. 1450-1459
[46] PengZ.HuJ.ShiK. et al.: ‘A novel optimal bipartite consensus control scheme for unknown multi‐agent systems via model‐free reinforcement learning’, Appl. Math. Comput., 2020, 369, p. 124821 · Zbl 1433.93008
[47] JianL.HuJ.WangJ. et al.: ‘Observer‐based output feedback distributed event‐triggered control for linear multi‐agent systems under general directed graphs’, Physica A, 2019, 534, p. 122288 · Zbl 07570700
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.