Abstract
In this study, we solve the finite-time leader-follower consensus problem of discrete-time second-order multi-agent systems (MASs) under the constraints of external disturbances. First, a novel consensus scheme is designed using a novel adaptive sliding mode control theory. Our adaptive controller is designed using the traditional sliding mode reaching law, and its advantages are chatter reduction and invariance to disturbances. In addition, the finite-time stability is demonstrated by presenting a discrete Lyapunov function. Finally, simulation results are presented to prove the validity of our theoretical results.
摘要
研究了离散时间二阶多智能体系统在外部干扰约束下的有限时间领导—跟随一致性问题。首先利用自适应滑模控制理论, 设计了一种新的有限时间一致性方案。自适应控制律是在传统滑模趋近律基础上改进设计的, 其优点是减少抖振并保持对干扰的不变性。此外, 通过给出一个离散李雅普诺夫函数, 证明了离散时间二阶多智能体系统的有限时间稳定性。最后, 数值模拟结果验证了理论分析的有效性。
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References
Atinç GM, Stipanović DM, Voulgaris PG, 2014. Supervised coverage control of multi-agent systems. Automatica, 50(11):2936–2942. https://doi.org/10.1016/j.automatica.2014.10.023
Chen SB, Beigi A, Yousefpour A, et al., 2020. Recurrent neural network-based robust nonsingular sliding mode control with input saturation for a non-holonomic spherical robot. IEEE Access, 8:188441–188453. https://doi.org/10.1109/ACCESS.2020.3030775
Chowdhury NR, Sukumar S, Chatterjee D, 2018. A new condition for asymptotic consensus over switching graphs. Automatica, 97:18–26. https://doi.org/10.1016/j.automatica.2018.07.018
Cruz-Piris L, Rivera D, Fernandez S, et al., 2018. Optimized sensor network and multi-agent decision support for smart traffic light management. Sensors, 18(2):435. https://doi.org/10.3390/s18020435
Cui GZ, Xu SY, Ma Q, et al., 2018. Command-filter-based distributed containment control of nonlinear multiagent systems with actuator failures. Int J Contr, 91(7):1708–1719. https://doi.org/10.1080/00207179.2017.1327722
Cui Q, Huang JS, Gao TT, 2020. Adaptive leaderless consensus control of uncertain multiagent systems with unknown control directions. Int J Robust Nonl Contr, 30(15):6229–6240. https://doi.org/10.1002/rnc.5083
Deng C, Er MJ, Yang GH, et al., 2020. Event-triggered consensus of linear multiagent systems with time-varying communication delays. IEEE Trans Cybern, 50(7):2916–2925. https://doi.org/10.1109/TCYB.2019.2922740
Fei Y, Shi P, Lim CC, 2020. Neural network adaptive dynamic sliding mode formation control of multi-agent systems. Int J Syst Sci, 51(11):2025–2040. https://doi.org/10.1080/00207721.2020.1783385
Gao WB, Wang YF, Homaifa A, 1995. Discrete-time variable structure control systems. IEEE Trans Ind Electron, 42(2):117–122. https://doi.org/10.1109/41.370376
Hamrah R, Sanya AK, Viswanathan SP, 2019. Discrete finite-time stable position tracking control of unmanned vehicles. Proc IEEE 58th Conf on Decision and Control, p.7025–7030. https://doi.org/10.1109/CDC40024.2019.9029700
Han GJ, Long XB, Zhu C, et al., 2020. A high-availability data collection scheme based on multi-AUVs for underwater sensor networks. IEEE Trans Mob Comput, 19(5):1010–1022. https://doi.org/10.1109/TMC.2019.2907854
Li P, Xu SY, Chu YM, et al., 2018. Finite-time leader-following rendezvous for Euler-Lagrange multi-agent systems with an uncertain leader. Trans Inst Meas Contr, 40(6):1766–1775. https://doi.org/10.1177/0142331217693918
Li Q, Xia LN, Song RZ, 2019a. Bipartite state synchronization of heterogeneous system with active leader on signed digraph under adversarial inputs. Neurocomputing, 369:69–79. https://doi.org/10.1016/j.neucom.2019.08.061
Li Q, Xia LN, Song RZ, 2019B. Output resilient containment control of heterogeneous systems with active leaders using reinforcement learning under attack inputs. IEEE Access, 7:162219–162228. https://doi.org/10.1109/ACCESS.2019.2947558
Li Q, Xia LN, Song RZ, et al., 2020. Leader-follower bipartite output synchronization on signed digraphs under adversarial factors via data-based reinforcement learning. IEEE Trans Neur Netw Learn Syst, 31(10):4185–4195. https://doi.org/10.1109/TNNLS.2019.2952611
Li Q, Xia LN, Song RZ, et al., 2021. Output event-triggered tracking synchronization of heterogeneous systems on directed digraph via model-free reinforcement learning. Inform Sci, 559:171–190. https://doi.org/10.1016/j.ins.2021.01.056
Li ZK, Duan ZS, Chen GR, et al., 2009. Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. IEEE Trans Circ Syst I Reg Papers, 57(1):213–224. https://doi.org/10.1109/TCSI.2009.2023937
Liang HJ, Liu GL, Zhang HG, et al., 2021. Neural-network-based event-triggered adaptive control of nonaffine nonlinear multiagent systems with dynamic uncertainties. IEEE Trans Neur Netw Learn Syst, 32(5):2239–2250. https://doi.org/10.1109/TNNLS.2020.3003950
Liu HY, Cheng L, Tan M, et al., 2020. Exponential finite-time consensus of fractional-order multiagent systems. IEEE Trans Syst Man Cybern Syst, 50(4):1549–1558. https://doi.org/10.1109/TSMC.2018.2816060
Liu JH, Wang CL, Cai X, 2019. Global finite-time event-triggered consensus for a class of second-order multiagent systems with the power of positive odd rational number and quantized control inputs. Neurocomputing, 360:254–264. https://doi.org/10.1016/j.neucom.2019.05.065
Liu JW, Huang J, 2021. Discrete-time leader-following consensus over switching digraphs with general system modes. IEEE Trans Autom Contr, 66(3):1238–1245. https://doi.org/10.1109/TAC.2020.2991696
Liu XY, Cao JD, Xie CL, 2019. Finite-time and fixed-time bipartite consensus of multi-agent systems under a unified discontinuous control protocol. J Franklin Inst, 356(2):734–751. https://doi.org/10.1016/j.jfranklin.2017.10.009
Liu YF, Su HS, 2021. Second-order consensus for multiagent systems with switched dynamics and sampled position data. IEEE Trans Syst Man Cybern Syst, 52(7):4129–4137. https://doi.org/10.1109/TSMC.2021.3089835
Lu JQ, Wang YQ, Shi XC, et al., 2021. Finite-time bipartite consensus for multiagent systems under detail-balanced antagonistic interactions. IEEE Trans Syst Man Cybern Syst, 51(6):3867–3875. https://doi.org/10.1109/tsmc.2019.2938419
Min HF, Xu SY, Li YM, et al., 2018. Adaptive finite-time control for stochastic nonlinear systems subject to unknown covariance noise. J Franklin Inst, 355(5):2645–2661. https://doi.org/10.1016/j.jfranklin.2018.02.003
Ning BD, Han QL, 2019. Prescribed finite-time consensus tracking for multiagent systems with nonholonomic chained-form dynamics. IEEE Trans Autom Contr, 64(4):1686–1693. https://doi.org/10.1109/TAC.2018.2852605
Oh KK, Park MC, Ahn HS, 2015. A survey of multi-agent formation control. Automatica, 53:424–440. https://doi.org/10.1016/j.automatica.2014.10.022
Olfati-Saber R, 2006. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans Autom Contr, 51(3):401–420. https://doi.org/10.1109/TAC.2005.864190
Olfati-Saber R, Murray RM, 2004. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Contr, 49(9):1520–1533. https://doi.org/10.1109/TAC.2004.834113
Olfati-Saber R, Fax JA, Murray RM, 2007. Consensus and cooperation in networked multi-agent systems. Proc IEEE, 95(1):215–233. https://doi.org/10.1109/JPROC.2006.887293
Qin JH, Zhang G, Zheng WX, et al., 2019. Adaptive sliding mode consensus tracking for second-order nonlinear multiagent systems with actuator faults. IEEE Trans Cybern, 49(5):1605–1615. https://doi.org/10.1109/TCYB.2018.2805167
Ren W, 2008. Consensus algorithms for double-integrator dynamics. IEEE Trans Autom Contr, 53(6):1503–1509. https://doi.org/10.1109/TAC.2008.924961
Ren W, Beard RW, 2008. Distributed Consensus in Multi-vehicle Cooperative Control. Springer, London, UK. https://doi.org/10.1007/978-1-84800-015-5
Shao XF, Ye D, 2021. Fuzzy adaptive event-triggered secure control for stochastic nonlinear high-order mass subject to DOS attacks and actuator faults. IEEE Trans Fuzzy Syst, 29(12):3812–3821. https://doi.org/10.1109/TFUZZ.2020.3028657
Shi S, Feng HY, Liu WH, et al., 2019. Finite-time consensus of high-order heterogeneous multi-agent systems with mismatched disturbances and nonlinear dynamics. Nonl Dynam, 96(2):1317–1333. https://doi.org/10.1007/s11071-019-04856-3
Sinha A, Mishra RK, 2020. Consensus in first order nonlinear heterogeneous multi-agent systems with event-based sliding mode control. Int J Contr, 93(4):858–871. https://doi.org/10.1080/00207179.2018.1531147
Sun ZJ, Zhang GQ, Lu Y, et al., 2018. Leader-follower formation control of underactuated surface vehicles based on sliding mode control and parameter estimation. ISA Trans, 72:15–24. https://doi.org/10.1016/j.isatra.2017.11.008
Tong P, Chen SH, Wang L, 2018. Finite-time consensus of multi-agent systems with continuous time-varying interaction topology. Neurocomputing, 284:187–193. https://doi.org/10.1016/j.neucom.2018.01.004
Tsai JSH, Fang JS, Yan JJ, et al., 2018. Hybrid robust discrete sliding mode control for generalized continuous chaotic systems subject to external disturbances. Nonl Anal Hybr Syst, 29:74–84. https://doi.org/10.1016/j.nahs.2018.01.001
Utkin V, 1977. Variable structure systems with sliding modes. IEEE Trans Autom Contr, 22(2):212–222. https://doi.org/10.1109/TAC.1977.1101446
Wang B, Tian YP, 2021. Consensus of discrete-time multiagent systems with multiplicative uncertainties and delays. Int J Syst Sci, 52(11):2311–2323. https://doi.org/10.1080/00207721.2021.1883766
Wang GD, Wang XY, Li SH, 2018. Sliding-mode consensus algorithms for disturbed second-order multi-agent systems. J Franklin Inst, 355(15):7443–7465. https://doi.org/10.1016/j.jfranklin.2018.07.027
Wang JY, Qiao JF, Wen GH, et al., 2021. Rendezvous of heterogeneous multiagent systems with nonuniform time-varying information delays: an adaptive approach. IEEE Trans Syst Man Cybern Syst, 51(8):4848–4857. https://doi.org/10.1109/tsmc.2019.2945592
Wang QL, Sun CY, 2020. Adaptive consensus of multiagent systems with unknown high-frequency gain signs under directed graphs. IEEE Trans Syst Man Cybern Syst, 50(6):2181–2186. https://doi.org/10.1109/TSMC.2018.2810089
Wang QS, Duan ZS, Lv YZ, et al., 2021. Linear quadratic optimal consensus of discrete-time multi-agent systems with optimal steady state: a distributed model predictive control approach. Automatica, 127:109505. https://doi.org/10.1016/j.automatica.2021.109505
Wang W, Liang HJ, Pan YN, et al., 2020. Prescribed performance adaptive fuzzy containment control for nonlinear multiagent systems using disturbance observer. IEEE Trans Cybern, 50(9):3879–3891. https://doi.org/10.1109/TCYB.2020.2969499
Wang XY, Li SH, Chen MZQ, 2018. Composite back-stepping consensus algorithms of leader-follower higherorder nonlinear multiagent systems subject to mismatched disturbances. IEEE Trans Cybern, 48(6):1935–1946. https://doi.org/10.1109/TCYB.2017.2720680
Wang YL, Jahanshahi H, Bekiros S, et al., 2021. Deep recurrent neural networks with finite-time terminal sliding mode control for a chaotic fractional-order financial system with market confidence. Chaos Sol Fract, 146: 110881. https://doi.org/10.1016/jxhaos.2021.110881
Xia LN, Li Q, Song RZ, et al., 2022a. Optimal synchronization control of heterogeneous asymmetric input-constrained unknown nonlinear mass via reinforcement learning. IEEE/CAA J Autom Sin, 9(3):520–532. https://doi.org/10.1109/JAS.2021.1004359
Xia LN, Li Q, Song RZ, et al., 2022B. Leader-follower time-varying output formation control of heterogeneous systems under cyber attack with active leader. Inform Sci, 585:24–40. https://doi.org/10.1016/j.ins.2021.11.026
Xie DS, Xu SY, Zhang BY, et al., 2016. Consensus for multi-agent systems with distributed adaptive control and an event-triggered communication strategy. IET Contr Theory Appl, 10(13):1547–1555. https://doi.org/10.1049/iet-cta.2015.1221
Xu Y, Wu ZG, 2021. Distributed adaptive event-triggered fault-tolerant synchronization for multiagent systems. IEEE Trans Ind Electron, 68(2):1537–1547. https://doi.org/10.1109/TIE.2020.2967739
Yao DY, Li HY, Lu RQ, et al., 2020. Distributed sliding-mode tracking control of second-order nonlinear multiagent systems: an event-triggered approach. IEEE Trans Cybern, 50(9):3892–3902. https://doi.org/10.1109/TCYB.2019.2963087
Young KD, Utkin VI, Ozguner U, 1999. A control engineer’s guide to sliding mode control. IEEE Trans Contr Syst Technol, 7(3):328–342. https://doi.org/10.1109/87.761053
Yu SH, Long XJ, 2015. Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode. Automatica, 54:158–165. https://doi.org/10.1016/j.automatica.2015.02.001
Zhang HG, Zhou Y, Liu Y, et al., 2020a. Cooperative bipartite containment control for multiagent systems based on adaptive distributed observer. IEEE Trans Cybern, 52(6):5432–5440. https://doi.org/10.1109/TCYB.2020.3031933
Zhang HG, Zhang J, Cai YL, et al., 2020b. Leader-following consensus for a class of nonlinear multiagent systems under event-triggered and edge-event triggered mechanisms. IEEE Trans Cybern, early access. https://doi.org/10.1109/TCYB.2020.3035907
Zhang HG, Duan J, Wang YC, et al., 2021a. Bipartite fixed-time output consensus of heterogeneous linear multiagent systems. IEEE Trans Cybern, 51(2):548–557. https://doi.org/10.1109/TCYB.2019.2936009
Zhang HG, Ren H, Mu YF, et al., 2021b. Optimal consensus control design for multiagent systems with multiple time delay using adaptive dynamic programming. IEEE Trans Cybern, early access. https://doi.org/10.1109/TCYB.2021.3090067
Zhang J, Zhang HG, Sun SX, et al., 2021. Leader-follower consensus control for linear multi-agent systems by fully distributed edge-event-triggered adaptive strategies. Inform Sci, 555:314–338. https://doi.org/10.1016/j.ins.2020.10.056
Zhang JL, Chen X, Gu GX, 2021. State consensus for discrete-time multiagent systems over time-varying graphs. IEEE Trans Autom Contr, 66(1):346–353. https://doi.org/10.1109/TAC.2020.2979750
Zhang WL, Mao S, Huang JH, et al., 2021. Data-driven resilient control for linear discrete-time multi-agent networks under unconfined cyber-attacks. IEEE Trans Circ Syst I Reg Papers, 68(2):776–785. https://doi.org/10.1109/TCSI.2020.3037242
Zhang YY, Li S, Liao LF, 2021. Consensus of high-order discrete-time multiagent systems with switching topology. IEEE Trans Syst Man Cybern Syst, 51(2):721–730. https://doi.org/10.1109/TSMC.2018.2882558
Zhang Z, Shi Y, Zhang ZX, et al., 2019. New results on sliding-mode control for Takagi-Sugeno fuzzy multiagent systems. IEEE Trans Cybern, 49(5):1592–1604. https://doi.org/10.1109/TCYB.2018.2804759
Zhou SS, Jahanshahi H, Din Q, et al., 2021. Discrete-time macroeconomic system: bifurcation analysis and synchronization using fuzzy-based activation feedback control. Chaos Sol Fract, 142:110378. https://doi.org/10.1016/j.chaos.2020.110378
Zou WC, Shi P, Xiang ZR, et al., 2020. Finite-time consensus of second-order switched nonlinear multi-agent systems. IEEE Trans Neur Netw Learn Syst, 31(5):1757–1762. https://doi.org/10.1109/TNNLS.2019.2920880
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Project supported by the National Natural Science Foundation of China (Nos. 61873300 and 61722312) and the Fundamental Research Funds for the Central Universities, China (Nos. FRF-MP-20-11 and FRF-IDRY-20-030)
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Ruizhuo SONG and Shi XING designed the research. Shi XING processed the data. Ruizhuo SONG, Shi XING, and Zhen XU drafted the paper. Ruizhuo SONG and Shi XING revised and finalized the paper.
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Ruizhuo SONG, Shi XING, and Zhen XU declare that they have no conflict of interest.
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Song, R., Xing, S. & Xu, Z. Finite-time leader-follower consensus of a discrete-time system via sliding mode control. Front Inform Technol Electron Eng 23, 1057–1068 (2022). https://doi.org/10.1631/FITEE.2100565
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DOI: https://doi.org/10.1631/FITEE.2100565