Abstract
We study the containment control problem for high-order heterogeneous nonlinear multi-agent systems under distributed event-triggered schemes. To achieve the containment control objective and reduce communication consumption among agents, a distributed event-triggered control scheme is proposed by applying the backstepping method, Lyapunov functional approach, and neural networks. Then, the results are extended to the self-triggered control case to avoid continuous monitoring of state errors. The developed protocols and triggered rules ensure that the output for each follower converges to the convex hull spanned by multi-leader signals within a bounded error. In addition, no agent exhibits Zeno behavior. Two numerical simulations are finally presented to verify the correctness of the obtained results.
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References
Chu HJ, Gao LX, Zhang WD, 2016. Distributed adaptive containment control of heterogeneous linear multi-agent systems: an output regulation approach. IET Contr Theory Appl, 10(1):95–102. https://doi.org/10.1049/iet-cta.2015.0398
Dimarogonas DV, Frazzoli E, Johansson KH, 2012. Distributed event-triggered control for multi-agent systems. IEEE Trans Autom Contr, 57(5):1291–1297. https://doi.org/10.1109/TAC.2011.2174666
Dolk V, Heemels M, 2017. Event-triggered control systems under packet losses. Automatica, 80:143–155. https://doi.org/10.1016/j.automatica.2017.02.029
Fan Y, Feng G, Wang Y, 2011. Combination framework of rendezvous algorithm for multi-agent systems with limited sensing ranges. Asian J Contr, 13(2):283–294. https://doi.org/10.1002/asjc.178
Fu JJ, Wang JZ, 2016. Robust finite-time containment control of general linear multi-agent systems under directed communication graphs. J Franklin Inst, 353(12):2670–2689. https://doi.org/10.1016/j.jfranklin.2016.05.015
Guo WL, 2016. Leader-following consensus of the second-order multi-agent systems under directed topology. ISA Trans, 65:116–124. https://doi.org/10.1016/j.isatra.2016.07.011
Haghshenas H, Badamchizadeh MA, Baradarannia M, 2015. Containment control of heterogeneous linear multiagent systems. Automatica, 54:210–216. https://doi.org/10.1016/j.automatica.2015.02.002
Hardy GH, Littlewood JE, Pólya G, 1952. Inequalities. Cambridge University Press, UK.
He XY, Wang QY, Yu WW, 2015. Distributed finite-time containment control for second-order nonlinear multiagent systems. Appl Math Comput, 268:509–521. https://doi.org/10.1016/j.amc.2015.06.101
Hu AH, Cao JD, Hu MF, et al., 2015. Event-triggered consensus of multi-agent systems with noises. J Franklin Inst, 352(9):3489–3503. https://doi.org/10.1016/j.jfranklin.2014.08.005
Ji M, Ferrari-Trecate G, Egerstedt M, et al., 2008. Containment control in mobile networks. IEEE Trans Autom Contr, 53(8):1972–1975. https://doi.org/10.1109/TAC.2008.930098
Li HL, Yang RN, Li QN, 2017. Designing a novel consensus protocol for multiagent systems with general dynamics under directed networks. Front Inform Technol Electron Eng, 18(8):1071–1081. https://doi.org/10.1631/FITEE.1601422
Li JZ, Li CL, Yang XF, et al., 2018. Event-triggered containment control of multi-agent systems with high-order dynamics and input delay. Electronics, 7(12):343. https://doi.org/10.3390/electronics7120343
Li WQ, Liu L, Feng G, 2016. Distributed containment tracking of multiple stochastic nonlinear systems. Automatica, 69:214–221. https://doi.org/10.1016/j.automatica.2016.02.021
Li WX, Chen ZQ, Liu ZX, 2014. Formation control for nonlinear multi-agent systems by robust output regulation. Neurocomputing, 140:114–120. https://doi.org/10.1016/j.neucom.2014.03.030
Li YF, Hua CC, Wu SS, et al., 2017. Output feedback distributed containment control for high-order nonlinear multiagent systems. IEEE Trans Cybern, 47(8):2032–2043. https://doi.org/10.1109/TCYB.2017.2655054
Lin X, Zheng YS, 2017. Finite-time consensus of switched multiagent systems. IEEE Trans Syst Man Cybern Syst, 47(7):1535–1545. https://doi.org/10.1109/TSMC.2016.2631659
Liu KE, Xie GM, Wang L, 2014. Containment control for second-order multi-agent systems with time-varying delays. Syst Contr Lett, 67:24–31. https://doi.org/10.1016/j.sysconle.2013.12.013
Liu YF, Geng ZY, 2015. Finite-time formation control for linear multi-agent systems: a motion planning approach. Syst Contr Lett, 85:54–60. https://doi.org/10.1016/j.sysconle.2015.08.009
Liu ZX, Jin QT, Chen ZQ, 2015. Distributed containment control for bounded unknown second-order nonlinear multi-agent systems with dynamic leaders. Neurocomputing, 168:1138–1143. https://doi.org/10.1016/j.neucom.2015.05.009
Lu MB, Liu L, 2019. Leader-following consensus of second-order nonlinear multi-agent systems subject to disturbances. Front Inform Technol Electron Eng, 20(1):88–94. https://doi.org/10.1631/FITEE.1800611
Ma CQ, Zhang JF, 2012. On formability of linear continuous-time multi-agent systems. J Syst Sci Compl, 25(1):13–29. https://doi.org/10.1007/s11424-012-0108-3
Ma Q, Miao GY, 2014. Distributed containment control of linear multi-agent systems. Neurocomputing, 133:399–403. https://doi.org/10.1016/j.neucom.2013.12.034
Meng ZY, Ren W, You Z, 2010. Distributed finite-time attitude containment control for multiple rigid bodies. Automatica, 46(12):2092–2099. https://doi.org/10.1016/j.automatica.2010.09.005
Miao GY, Cao JD, Alsaedi A, et al., 2017. Event-triggered containment control for multi-agent systems with constant time delays. J Franklin Inst, 354(15):6956–6977. https://doi.org/10.1016/j.jfranklin.2017.08.010
Qin JH, Yu CB, Anderson BDO, 2016. On leaderless and leader-following consensus for interacting clusters of second-order multi-agent systems. Automatica, 74:214–221. https://doi.org/10.1016/j.automatica.2016.07.008
Qin JH, Zheng WX, Gao HJ, et al., 2017. Containment control for second-order multiagent systems communicating over heterogeneous networks. IEEE Trans Neur Netw Learn Syst, 28(9):2143–2155. https://doi.org/10.1109/TNNLS.2016.2574830
Rehan M, Jameel A, Ahn CK, 2018. Distributed consensus control of one-sided Lipschitz nonlinear multiagent systems. IEEE Trans Syst Man Cybern Syst, 48(8):1297–1308. https://doi.org/10.1109/TSMC.2017.2667701
Tabuada P, 2007. Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans Autom Contr, 52(9):1680–1685. https://doi.org/10.1109/TAC.2007.904277
Wang P, Jia Y, 2015. Robust H∞ containment control for second-order multi-agent systems with nonlinear dynamics in directed networks. Neurocomputing, 153:235–241. https://doi.org/10.1016/j.neucom.2014.11.031
Wang W, Wang D, Peng Z, 2015. Distributed containment control for uncertain nonlinear multi-agent systems in non-affine pure-feedback form under switching topologies. Neurocomputing, 152:1–10. https://doi.org/10.1016/j.neucom.2014.11.035
Wang ZD, Ding DR, Dong HL, et al., 2013. H∞ consensus control for multi-agent systems with missing measurements: the finite-horizon case. Syst Contr Lett, 62(10):827–836. https://doi.org/10.1016/j.sysconle.2013.06.004
Wei B, Xiao F, 2016. Event-triggered control for synchronization of coupled harmonic oscillators. Syst Contr Lett, 97:163–168. https://doi.org/10.1016/j.sysconle.2016.09.006
Wu Z, Xu Y, Lu R, et al., 2018a. Event-triggered control for consensus of multiagent systems with fixed/switching topologies. IEEE Trans Syst Man Cybern Syst, 48(10):1736–1746. https://doi.org/10.1109/TSMC.2017.2744671
Wu Z, Xu Y, Pan Y, et al., 2018b. Event-triggered control for consensus problem in multi-agent systems with quantized relative state measurements and external disturbance. IEEE Trans Circ Syst I, 65(7):2232–2242. https://doi.org/10.1109/TCSI.2017.2777504
Xia H, Zheng WX, Shao JL, 2018. Event-triggered containment control for second-order multi-agent systems with sampled position data. ISA Trans, 73:91–99. https://doi.org/10.1016/j.isatra.2017.11.001
Xu HH, Zhu J, 2011. An iterative approach to Bayes risk decoding and system combination. J Zhejiang Univ-Sci C (Comput & Electron), 12(3):204–212. https://doi.org/10.1631/jzus.C1000045
Yan HC, Shen YC, Zhang H, et al., 2014. Decentralized event-triggered consensus control for second-order multi-agent systems. Neurocomputing, 133:18–24. https://doi.org/10.1016/j.neucom.2013.11.036
Yoo SJ, 2013. Distributed adaptive containment control of uncertain nonlinear multi-agent systems in strict-feedback form. Automatica, 49(7):2145–2153. https://doi.org/10.1016/j.automatica.2013.03.007
Zhang T, Ge SS, Hang CC, 2000. Adaptive neural network control for strict-feedback nonlinear systems using backstepping design. Automatica, 36(12):1835–1846. https://doi.org/10.1016/S0005-1098(00)00116-3
Zhang WB, Tang Y, Liu YR, et al., 2017. Event-triggering containment control for a class of multi-agent networks with fixed and switching topologies. IEEE Trans Circ Syst I, 64(3):619–629. https://doi.org/10.1109/TCSI.2016.2618944
Zheng YS, Ma JY, Wang L, 2018. Consensus of hybrid multi-agent systems. IEEE Trans Neur Netw Learn Syst, 29(4):1359–1365. https://doi.org/10.1109/TNNLS.2017.2651402
Zhou F, Wang ZJ, 2015. Containment control of linear multi-agent systems with directed graphs and multiple leaders of time-varying bounded inputs. IET Contr Theory Appl, 9(16):2466–2473. https://doi.org/10.1049/iet-cta.2014.0634
Zou WC, Xiang ZR, 2017. Event-triggered distributed containment control of heterogeneous linear multi-agent systems by an output regulation approach. Int J Syst Sci, 48(10):2041–2054. https://doi.org/10.1080/00207721.2017.1309595
Zou WC, Xiang ZR, 2019a. Event-triggered containment control of second-order nonlinear multi-agent systems. J Franklin Inst, 356(17):10421–10438. https://doi.org/10.1016/j.jfranklin.2018.05.060
Zou WC, Xiang ZR, 2019b. Event-triggered leader-following consensus of non-linear multi-agent systems with switched dynamics. IET Contr Theory Appl, 13(9):1222–1228. https://doi.org/10.1049/iet-cta.2018.5126
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Project supported by the National Natural Science Foundation of China (Nos. 61873128 and 61673219) and the Jiangsu Key Research and Development Plan, China (No. BE2018004-3)
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Zheng-rong XIANG provided the idea. Ya-ni SUN designed the research. Ya-ni SUN and Wen-cheng ZOU conducted the simulations. Ya-ni SUN drafted the manuscript. Jian GUO and Zheng-rong XIANG helped organize the manuscript. Ya-ni SUN and Zheng-rong XIANG revised and finalized the paper.
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Ya-ni SUN, Wen-cheng ZOU, Jian GUO, and Zheng-rong XIANG declare that they have no conflict of interest.
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Sun, Yn., Zou, Wc., Guo, J. et al. Containment control for heterogeneous nonlinear multi-agent systems under distributed event-triggered schemes. Front Inform Technol Electron Eng 22, 107–119 (2021). https://doi.org/10.1631/FITEE.2000034
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DOI: https://doi.org/10.1631/FITEE.2000034
Key words
- Multi-agent systems
- Distributed event-triggered control
- Containment control
- Heterogeneous nonlinear systems
- Zeno behavior