Abstract
In this manuscript, the stability and consensus problem of the leader-following multi-agent system is studied. The state information of the leader is only available to the dynamics of all the followers, while the communication among the agents occurs at sampling instant. The innovative part of this paper is to reach the consensus and attain the stability for prescribed MASs with interval time varying delay using impulsive control in the presence of leader. The interaction between the agent is illustrated by an undirected graph. A class of distributed impulsive protocol relying on sampling information is suggested to reach the leader following consensus. The consensus is critically relying on the sampling period, control gains. By performing the similar procedures, the consensus problem of multi-agent system is converted to stability problem of the error system. By utilizing the stability theory of impulsive systems, algebraic graph theory, sufficient conditions are derived to guarantee the leader-following consensus of the multi-agent system. Terminally, a numerical example is given to show an efficacy of this presented approach and the sureness of theoretical analysis.
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References
Chen YQ, Wang Z (2005) Formation control: a review and a new consideration. In: IEEE/RSJ international conference on intelligent robots and systems (IROS), pp 3181–3186
Ren W, Beard R, Atkins E (2007) Information consensus in multivehicle cooperative control. IEEE Control Syst Mag 27:71–82
Ren W, Beard R (2005) Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans Autom Control 50:655–661
Li ZK, Ren W, Liu XD, Fu MY (2013) Consensus of multi-agent systems with general linear and lipschitz nonlinear dynamics using distributed adaptive protocols. IEEE Trans Autom Control 58:1786–1791
Cao Y, Ren W (2012) Distributed coordinated tracking with reduced interaction via a variable structure approach. IEEE Trans Autom Control 57:33–48
Fax JA, Murray RM (2004) Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control 49:1465–1476
Song Q, Cao J, Yu W (2010) Second-order leader-following consensus of nonlinear multi-agent systems via pinning control. Syst Control Lett 59:553–562
Angeli D, Bliman PA (2006) Stability of leaderless discrete-time multi-agent systems. Math Control Signals Syst 18:293–322
Meng Z, Ren W, Cao Y, You Z (2011) Leaderless and leaderfollowing consensus with communication and input delays under a directed network topology. IEEE Trans Syst Man Cybern B 41:75–88
Cheng L, Wang Y, Ren W, Hou Z, Tan M (2016) On convergence rate of leader-following consensus of linear multi-agent systems with communication noises. IEEE Trans Autom Control 61:3586–3592
Cheng L, Wang Y, Ren W, Hou Z, Tan M (2014) Containment control of multi-agent systems with dynamic leaders based on a \(PI^n\)-type approach. IEEE Trans Cybern 46:3004–3017
Li Z, Duan Z, Chen G (2011) Dynamic consensus of linear multi-agent systems. IET Control Theory Appl 5:19–28
Yu W, Ren W, Zheng WX (2013) Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics. Automatica 49:2107–2115
Yu W, Chen G, Cao M, Kurths J (2010) Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics. IEEE Trans Syst Man Cybern Part B Cybern 40:881–891
Wen GH, Hu GQ, Yu WW, Chen GR (2014) Distributed H\(\infty \) consensus of higher order multiagent systems with switching topologies. IEEE Trans Circuits Syst Express Briefs 61:359–363
Seo J, Shim H, Back J (2009) Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach. Automatica 45:2659–2664
Nagamani G, Balasubramaniam P (2012) Delay-dependent passivity criteria for uncertain switched neural networks of neutral type with interval time-varying delay. Phys Scr 85:045010
Song Q, Cao J (2012) Passivity of uncertain neural networks with both leakage delay and time-varying delay. Nonlinear Dyn 67:1695–1707
Chen X, Song Q, Liu X, Zhao Z (2014) Global-stability of complex-valued neural networks with unbounded time-varying delays. Abstract and Applied Analysis
Zhu Q, Cao J (2010) Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays. Neurocomputing 73:2671–2680
Zhu W, Cheng D (2010) Leader-following consensus of second-order agents with multiple time-varying delays. Automatica 46:1994–1999
Chen CLP, Wen GX, Liu YJ, Wang FY (2014) Adaptive consensus control for a class of nonlinear multiagent time-delay systems using neural networks. IEEE Trans Neural Netw Learn Syst 25:1217–1226
Peng K, Yang Y (2009) Leader-following consensus problem with a varying-velocity leader and time-varying delays. Physica A 388:193–208
Gao X, Wang L (2011) Sampled data based consensus of continuous-time multiagent systems with time-varying topology. IEEE Trans Autom Control 56:1226–1231
Sui X, Yang Y, Xu X, Zhang S, Zhang L (2017) The sampled-data consensus of multi-agent systems with probabilistic time-varying delays and packet losses. Physica A Stat Mech Appl 492:1625–1641
Zhang Y, Tian YP (2010) Consensus of data-sampled multiagent systems with random communication delay and packet loss. IEEE Trans Autom Control 55:939–943
Song Q, Cao J, Yu W (2010) Second-order leader-following consensus of nonlinear multi-agent systems via pinning control. Syst Control Lett 59:553–562
Yu W, Zheng WX, Chen G, Ren W, Cao J (2011) Second-order consensus in multi-agent dynamical systems with sampled position data. Automatica 47:1496–1503
Syed Ali M, Gunasekaran N, Zhu Q (2017) State estimation of T–S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control. Fuzzy Sets Syst 306:87–104
Yu W, Wang H, Cheng F, Yu X, Wen G (2017) Second-order consensus in multiagent systems via distributed sliding mode control. IEEE Trans Cybern 47:1872–1881
Li H, Su H (2015) Distributed consensus of multi-agent systems with nonlinear dynamics via adaptive intermittent control. J Franklin Inst 352:4546–4564
Guo XG, Wang JL, Liao F (2015) Non-fragile \(H_{\infty }\) consensus of linear multi-agent systems with interval-bounded variations. In: 23rd Mediterranean conference on control and automation
Hu A, Cao J, Hu M, Guo L (2015) Event-triggered consensus of Markovian jumping multi-agent systems via stochastic sampling. IET Control Theory Appl 9:1964–1972
Nagamani G, Radhika T, Gopalakrishnan P (2016) Dissipativity and passivity analysis of Markovian jump impulsive neural networks with time delays. Int J Comput Math 94:1479–1500
Li X, Chen Z (2009) Stability properties for Hopfield neural networks with delays and impulsive perturbations. Nonlinear Anal Real World Appl 10:3253–3265
Fu X, Li X (2011) LMI conditions for stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays. Commun Nonlinear Sci Numer Simul 16:435–454
Fu X, Li X (2009) Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays. J Comput Appl Math 231:187–199
Li X, Regan DO, Akca H (2015) Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays. IMA J Appl Math 80:85–99
Guan ZH, Liu ZW, Feng G (2012) Impulsive consensus algorithms for second-order multi-agent networks with sampled information. Automatica 48:1397–1404
Ding L, Yu P, Liu ZW, Guan ZH, Feng G (2013) Consensus of second-order multi-agent systems via impulsive control using sampled hetero-information. Automatica 49:2881–2886
Ma TD, Zhang LY, Zhao FY, Gu ZY, Xu YX (2015) Impulsive consensus of multi-agent nonlinear systems with control gain error. Neurocomputing 171:293–298
Zhang L, Li T, Huang T, Huang J, Ma T (2107) Adaptive impulsive consensus of multi-agent systems with control gain error
Hu HX, Liu A, Xuan Q, Yu L, Xie G (2015) Second-order consensus of multi-agent systems in the cooperation competition network with switching topologies: A time-delayed impulsive control approach. Syst Control Lett 62:1125–1135
Syed Ali M, Vadivel R, Kwon OM (2019) Decentralised event-triggered impulsive synchronisation for semi-Markovian jump delayed neural networks with leakage delay and randomly occurring uncertainties. Int J Syst Sci 50:1636–1660
Dharani S, Balasubramaniam P (2019) Delayed impulsive control for exponential synchronization of stochastic reaction–diffusion neural networks with time-varying delays using general integral inequalities. Neural Comput Appl 31:8719–8726
Zhao H, Li L, Peng H, Xiao J, Yang Y, Zheng M (2016) Impulsive control for synchronization and parameters identification of uncertain multi-links complex network. Nonlinear Dyn 83:1437–1451
Qin W, Liu Z, Chen Z (2015) Impulsive observer-based consensus control for multi-agent systems with time delay. Int J Control 88:1789–1804
Syed Ali M, Gunasekaran N, Esther Rani M (2017) Robust stability of Hopfield delayed neural networks via an augmented L–K functional. Neurocomputing 234:198–204
Li H (2016) Leader-following consensus of nonlinear multi-agent systems with mixed delays and uncertain parameters via adaptive pinning intermittent control. Nonlinear Anal Hybrid Syst 22:202–214
Wang Y, Yi J-W (2014) Consensus in second-order multi-agent systems via impulsive control using position-only information with heterogeneous delays. IET Control Theory Appl 9:336–345
Kwon OM, Park JH, Lee SM, Cha EJ (2014) New augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays. Nonlinear Dyn 76:221–236
Seuret A, Gouaisbaut F (2013) Wirtinger-based integral inequality: application to time-delay systems. Automatica 49:2860–2866
Gu K, Kharitonov VL, Chen J (2003) Stability of time-delay systems. Birkhauser, Boston
Ali MS, Saravanakumar R (2014) Improved delay-dependent robust \(H_\infty \) control of an uncertain stochastic system with interval time varying and distributed delays. Chin Phys B 23:120201
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The work of author was supported by SERB – MATRICS Project No. MTR/2018/000931.
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Ali, M.S., Agalya, R., Orman, Z. et al. Leader-Following Consensus of Non-linear Multi-agent Systems with Interval Time-Varying Delay via Impulsive Control. Neural Process Lett 53, 69–83 (2021). https://doi.org/10.1007/s11063-020-10384-8
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DOI: https://doi.org/10.1007/s11063-020-10384-8