Abstract: In this study, we discuss how multi-agent systems (MASs) with a leader can achieve distributed bipartite tracking consensus using asynchronous impulsive control strategies. The proposed asynchronous impulsive control approach does not require the impulse to occur simultaneously for all agents. The communication links between neighboring nodes of MASs are antagonistic. When the leader’s control input is non-zero, sufficient conditions are obtained to achieve bipartite asynchronous impulsive tracking consensus in closed-loop MASs. More extensive ranges of asynchronous impulsive effects are discussed, and the designed controller’s feedback can effectively work against adverse impulsive permutation. Simple algebraic conditions for estimating the impulsive gain boundary and asynchronous impulsive interval are presented. Theoretical results are demonstrated with illustrative examples.

多智能体系统的二分异步脉冲跟踪一致性

[1]Altafini C, 2013. Consensus problems on networks with antagonistic interactions. IEEE Trans Automat Contr, 58(4):935-946.

[2]Du HB, Wen GH, Wu D, et al., 2020. Distributed fixed-time consensus for nonlinear heterogeneous multi-agent systems. Automatica, 113:108797.

[3]Gao F, Chen WS, Li ZW, et al., 2020. Neural network-based distributed cooperative learning control for multiagent systems via event-triggered communication. IEEE Trans Neur Netw Learn Syst, 31(2):407-419.

[4]Guan ZH, Hu B, Chi M, et al., 2014. Guaranteed performance consensus in second-order multi-agent systems with hybrid impulsive control. Automatica, 50(9):2415-2418.

[5]Han XP, Zhao YS, Li XD, 2020. A survey on complex dynamical networks with impulsive effects. Front Inform Technol Electron Eng, 21(2):199-219.

[6]He WL, Qian F, Lam J, et al., 2015. Quasi-synchronization of heterogeneous dynamic networks via distributed impulsive control: error estimation, optimization and design. Automatica, 62:249-262.

[7]Hong HF, Wang H, Wang ZL, et al., 2019. Finite-time and fixed-time consensus problems for second-order multi-agent systems with reduced state information. Sci China Inform Sci, 62(11):212201.

[8]Hu X, Zhang ZF, Li CD, 2021. Consensus of multi-agent systems with dynamic join characteristics under impulsive control. Front Inform Technol Electron Eng, 22(1):120-133.

[9]Jadbabaie A, Lin J, Morse AS, 2003. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Automat Contr, 48(6):988-1001.

[10]Ji XR, Lu JQ, Lou JG, et al., 2020. A unified criterion for global exponential stability of quaternion-valued neural networks with hybrid impulses. Int J Robust Nonl Contr, 30(18):8098-8116.

[11]Jiang BX, Lu JQ, Liu Y, 2020. Exponential stability of delayed systems with average-delay impulses. SIAM J Contr Optim, 58(6):3763-3784.

[12]Jiang FC, Liu B, Wu YJ, et al., 2018. Asynchronous consensus of second-order multi-agent systems with impulsive control and measurement time-delays. Neurocomputing, 275:932-939.

[13]Jiang Y, Zhang HW, Chen J, 2017. Sign-consensus of linear multi-agent systems over signed directed graphs. IEEE Trans Ind Electron, 64(6):5075-5083.

[14]Lakshmikantham V, Bainov DD, Simeonov PS, 1989. Theory of Impulsive Differential Equations. World Scientific Publishing, Singapore Teaneck, USA.

[15]Li K, Hua CC, You X, et al., 2020. Output feedback-based consensus control for nonlinear time delay multiagent systems. Automatica, 111:108669.

[16]Li XD, Ho DWC, Cao JD, 2019a. Finite-time stability and settling-time estimation of nonlinear impulsive systems. Automatica, 99:361-368.

[17]Li XD, Yang XY, Huang TW, 2019b. Persistence of delayed cooperative models: impulsive control method. Appl Math Comput, 342:130-146.

[18]Li XD, Peng DX, Cao JD, 2020. Lyapunov stability for impulsive systems via event-triggered impulsive control. IEEE Trans Automat Contr, 65(11):4908-4913.

[19]Li YY, 2017. Impulsive synchronization of stochastic neural networks via controlling partial states. Neur Process Lett, 46(1):59-69.

[20]Liu F, Song Q, Wen GH, et al., 2018. Bipartite synchronization in coupled delayed neural networks under pinning control. Neur Netw, 108:146-154.

[21]Liu ZW, Hu X, Ge MF, et al., 2019. Asynchronous impulsive control for consensus of second-order multi-agent networks. Commun Nonl Sci Numer Simul, 79:104892.

[22]Lu JQ, Ho DWC, Cao JD, 2010. A unified synchronization criterion for impulsive dynamical networks. Automatica, 46(7):1215-1221.

[23]Lu JQ, Wang ZD, Cao JD, et al., 2012. Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int J Bifurcat Chaos, 22(7):1250176.

[24]Lu WL, Li X, Rong ZH, 2010. Global stabilization of complex networks with digraph topologies via a local pinning algorithm. Automatica, 46(1):116-121.

[25]Meng DY, 2017. Bipartite containment tracking of signed networks. Automatica, 79:282-289.

[26]Ning BD, Han QL, Zuo ZY, 2019. Practical fixed-time consensus for integrator-type multi-agent systems: a time base generator approach. Automatica, 105:406-414.

[27]Ning BD, Han QL, Zuo ZY, 2020. Bipartite consensus tracking for second-order multi-agent systems: a time-varying function based preset-time approach. IEEE Trans Automat Contr, 66(6):2739-2745.

[28]Pan LL, Shao HB, Xi YG, et al., 2021. Bipartite consensus problem on matrix-valued weighted directed networks. Sci China Inform Sci, 64(4):149204.

[29]Tan XG, Cao JD, Li XD, 2019. Consensus of leader-following multiagent systems: a distributed event-triggered impulsive control strategy. IEEE Trans Cybern, 49(3):792-801.

[30]Wang P, Li XC, Wang N, et al., 2021. Almost periodic synchronization of quaternion-valued fuzzy cellular neural networks with leakage delays. Fuzzy Sets Syst, 426:46-65.

[31]Wang YQ, Lu JQ, Liang JL, et al., 2019. Pinning synchronization of nonlinear coupled Lur’e networks under hybrid impulses. IEEE Trans Circ Syst II, 66(3):432-436.

[32]Wen GH, Wang H, Yu XH, et al., 2018. Bipartite tracking consensus of linear multi-agent systems with a dynamic leader. IEEE Trans Circ Syst II, 65(9):1204-1208.

[33]Yang D, Li XD, Qiu JL, 2019. Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback. Nonl Anal Hybrid Syst, 32:294-305.

[34]Yang T, Chua LO, 1997. Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans Circ Syst I, 44(10):976-988.

[35]Yang XS, Lu JQ, Ho DWC, et al., 2018. Synchronization of uncertain hybrid switching and impulsive complex networks. Appl Math Model, 59:379-392.

[36]Yang XS, Li XD, Lu JQ, et al., 2020. Synchronization of time-delayed complex networks with switching topology via hybrid actuator fault and impulsive effects control. IEEE Trans Cybern, 50(9):4043-4052.

[37]Yang ZQ, Pan XF, Zhang Q, et al., 2021. Finite-time formation control for first-order multi-agent systems with region constraints. Front Inform Technol Electron Eng, 22(1):134-140.

[38]Yu WW, Li Y, Wen GH, et al., 2017. Observer design for tracking consensus in second-order multi-agent systems: fractional order less than two. IEEE Trans Automat Contr, 62(2):894-900.

[39]Zahreddine Z, 2003. Matrix measure and application to stability of matrices and interval dynamical systems. Int J Math Math Sci, 2003:937084.

[40]Zhang H, Ji HH, Ye ZY, et al., 2017. Impulsive consensus of multi-agent systems with stochastically switching topologies. Nonl Anal Hybrid Syst, 26:212-224.

[41]Zhang LZ, Yang YQ, 2020. Impulsive effects on bipartite quasi synchronization of extended Caputo fractional order coupled networks. J Franklin Inst, 357(7):4328-4348.

[42]Zhao L, Yang GH, 2020. Cooperative adaptive fault-tolerant control for multi-agent systems with deception attacks. J Franklin Inst, 357(6):3419-3433.

[43]Zhou KM, Doyle JC, 1998. Essentials of Robust Control. Prentice Hall, Upper Saddle River, USA.

[44]Zhu W, Zhou QH, Li QD, 2020. Asynchronous consensus of linear multi-agent systems with impulses effect. Commun Nonl Sci Numer Simul, 82:105044.

[45]Zhu YN, Yu WW, Wen GH, et al., 2020. Distributed Nash equilibrium seeking in an aggregative game on a directed graph. IEEE Trans Automat Contr, 66(6):2746-2753.

[46]Zuo ZY, Han QL, Ning BD, et al., 2018. An overview of recent advances in fixed-time cooperative control of multiagent systems. IEEE Trans Ind Inform, 14(6):2322-2334.