具有输入时滞的MAS预设时间滞后一致性

doi:10.12305/j.issn.1001-506X.2025.09.25

摘要/Abstract

摘要：

针对存在输入时滞的多智能体系统（multi-agent system，MAS）滞后一致性问题，提出一种基于时基生成器（time base generator，TBG）的二阶MAS预设时间领导跟随滞后一致性控制方法，使得稳定时间与系统初始状态无关且可预先设定。首先，提出一种误差变换方法，将具有时滞的误差系统转换为无时滞误差系统。然后，利用TBG函数构造误差辅助变量并构造相应滑模面，进而设计预设时间控制器。同时，证明所设计控制器的预设时间稳定性。最后，通过数值仿真验证所提方法的可行性及有效性。仿真结果表明，MAS能够实现精确的预设时间滞后一致性。

关键词: 多智能体系统, 预设时间滞后一致性, 输入时滞, 时基生成器

Abstract:

To solve the lag consensus problem of multi-agent system （MAS） with input delay, a second-order MAS predefined-time leader-following lag consensus control method based on time base generator （TBG） is proposed, which makes the settling time independent of the initial state of the system and can be predefined in advance. Firstly, an error transformation method is proposed to transform the error system with delay into the delay-free error system. Secondly, the TBG function is used to construct the error auxiliary variable and construct the corresponding sliding mode surface. Then, the predefined-time controller is designed and the stability of the predefined-time controller is proved. Finally, the feasibility and effectiveness of the proposed method are verified by numerical simulation. Simulation result shows that the MAS can achieves accurate predefined-time lag consensus.

Key words: multi-agent system (MAS), predefined-time lag consensus, input delay, time base generator (TBG)

中图分类号:

TP 13

郭方杰, 李靖, 张朝辉. 具有输入时滞的MAS预设时间滞后一致性[J]. 系统工程与电子技术, 2025, 47(9): 3041-3046.

Fangjie GUO, Jing LI, Zhaohui ZHANG. Predefined-time lag consensus for MAS with input delay[J]. Systems Engineering and Electronics, 2025, 47(9): 3041-3046.

图/表 5

参考文献 31

1	NING B, HAN Q L, LU Q, et al. Cooperative control of multirobot systems subject to control gain uncertainty[J]. IEEE Trans. on Industrial Informatics, 2022, 19 (4): 5367- 5376.
2	CAO Y C, YU W W, REN W, et al. An overview of recent progress in the study of distributed multi-agent coordination[J]. IEEE Trans. on Industrial informatics, 2012, 9 (1): 427- 438.
3	DING L, HAN Q L, GUO G. Network-based leader-following consensus for distributed multi-agent systems[J]. Automatica, 2013, 49 (7): 2281- 2286. doi: 10.1016/j.automatica.2013.04.021
4	赵芷若, 曹雷, 陈希亮, 等. 基于多智能体博弈强化学习的无人机智能攻击策略生成模型[J]. 系统工程与电子技术, 2023, 45 (10): 3165- 3171.
	ZHAO Z R, CAO L, CHEN X L, et al. UAV intelligent attack strategy generation model based on multi-agent game reinforcement learning[J]. Systems Engineering and Electronics, 2023, 45 (10): 3165- 3171.
5	马悦, 吴琳, 许霄. 基于多智能体强化学习的协同目标分配[J]. 系统工程与电子技术, 2023, 45 (9): 2793- 2801.
	MA Y, WU L, XU X. Cooperative targets assignment based on multi-agent reinforcement learning[J]. Systems Engineering and Electronics, 2023, 45 (9): 2793- 2801.
6	ZHANG Z, CHEN S M, ZHENG Y S. Fully distributed scaled consensus tracking of high-order multiagent systems with time delays and disturbances[J]. IEEE Trans. on Industrial Informatics, 2022, 18 (1): 305- 314. doi: 10.1109/TII.2021.3069207
7	张杰, 刘开蓉, 陈金宝, 等. 基于空间对抗的多智能体编队控制方法[J]. 系统工程与电子技术, 2024, 46 (6): 2082- 2091.
	ZHANG J, LIU K R, CHEN J B, et al. Multi-agents formation control method based on space confrontation[J]. Systems Engineering and Electronics, 2024, 46 (6): 2082- 2091.
8	罗哲, 权婉珍, 张朴睿, 等. 单边Lipschitz非线性多智能体系统一致性追踪控制[J]. 系统工程与电子技术, 2022, 44 (1): 279- 284. doi: 10.12305/j.issn.1001-506X.2022.01.34
	LUO Z, QUAN W Z, ZHANG P R, et al. Consensus tracking control for one-side Lipschitz nonlinear multi-agent systems[J]. Systems Engineering and Electronics, 2022, 44 (1): 279- 284. doi: 10.12305/j.issn.1001-506X.2022.01.34
9	WANG X J, NIU B, WANG H Q, et al. Prescribed performance-based finite-time consensus technology of nonlinear multiagent systems and application to FDPs[J]. IEEE Trans. on Circuits and Systems II: Express Briefs, 2023, 70 (2): 591- 595.
10	张普, 薛惠锋, 高山, 等. 具有混合执行器故障的多智能体分布式有限时间自适应协同容错控制[J]. 系统工程与电子技术, 2022, 44 (4): 1220- 1229. doi: 10.12305/j.issn.1001-506X.2022.04.19
	ZHANG P, XUE H F, GAO S, et al. Distributed finite-time adaptive cooperative fault-tolerant control for multi-agent systems with integrated actuators faults[J]. Systems Engineering and Electronics, 2022, 44 (4): 1220- 1229. doi: 10.12305/j.issn.1001-506X.2022.04.19
11	SEDGHI F, AREFI M M, ABOOEE A, et al. Distributed adaptive-neural finite time consensus control for stochastic nonlinear multiagent systems subject to saturated inputs[J]. IEEE Trans. on Neural Networks and Learning Systems, 2023, 34 (10): 7704- 7718. doi: 10.1109/TNNLS.2022.3145975
12	CHEN W, DU H, CHEN C C. Stability and robustness analysis of finite-time consensus algorithm for second-order multiagent systems under sampled-data control[J]. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2022, 53 (3): 1445- 1452.
13	LI H Y, LI X. Distributed fixed-time consensus of discrete-time heterogeneous multi-agent systems via predictive mechanism and Lyapu-nov approach[J]. IEEE Trans. on Circuits and Systems II: Express Briefs, 2024, 70 (1): 321- 325.
14	ZUO Z, KE R, HAN Q L. Fully distributed adaptive practical fixed-time consensus protocols for multi-agent systems[J]. Automatica, 2023, 157 (3): 111248.
15	POLYAKOV A. Nonlinear feedback design for fixed-time stabilization of linear control systems[J]. IEEE Trans. on Automatic Control, 2012, 57 (8): 2106- 2110. doi: 10.1109/TAC.2011.2179869
16	LV Y Z, WEN G H, HUANG T W. Adaptive protocol design for distributed tracking with relative output information: a distributed fixed-time observer approach[J]. IEEE Trans. on Control of Network Systems, 2020, 7 (1): 118- 128. doi: 10.1109/TCNS.2019.2919855
17	NING B, HAN Q L, ZUO Z. Distributed optimization for multiagent systems: an edge-based fixed-time consensus approach[J]. IEEE Trans. on Cybernetics, 2019, 49 (1): 122- 132. doi: 10.1109/TCYB.2017.2766762
18	SONG Y D, WANG Y J, HOLLOWAY J, et al. Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time[J]. Automatica, 2017, 83, 243- 251. doi: 10.1016/j.automatica.2017.06.008
19	SNCHEZ-TORRES J D, SANCHEZ E N, LOUKIANOV A G. Predefined-time stability of dynamical systems with sliding modes[C]// Proc. of the IEEE American Control Conference, 2015: 5842−5846.
20	BECERRA H M, VZQUEZ C R, ARECHAVALETA G, et al. Predefined-time convergence control for high-order integrator systems using time base generators[J]. IEEE Trans. on Control Systems Technology, 2018, 26 (5): 1866- 1873. doi: 10.1109/TCST.2017.2734050
21	SHAKOURI A, ASSADIAN N. Prescribed-time control for perturbed Euler Lagrange systems with obstacle avoidance[J]. IEEE Trans. on Automatic Control, 2022, 67 (7): 3754- 3761. doi: 10.1109/TAC.2021.3106882
22	NING B, HAN Q L, ZUO Z. Bipartite consensus tracking for second-order multiagent systems: a time-varying function-based preset-time approach[J]. IEEE Trans. on Automatic Control, 2021, 66 (6): 2739- 2745. doi: 10.1109/TAC.2020.3008125
23	GUO Z J, CHEN G. Predefined-time distributed optimal allocation of resources: a time-base generator scheme[J]. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2022, 52 (1): 438- 447.
24	GUO C Q, HU J P. Time base generator based practical predefined-time stabilization of high-order systems with unknown disturbance[J]. IEEE Trans. on Circuits and Systems II: Express Briefs, 2023, 70 (7): 2670- 2674.
25	YU J Y, XIAO F, CAO M T. Lag group consensus of high-order multiagent systems in directed network settings[J]. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2023, 53 (7): 4442- 4452.
26	WANG Y, MA Z J, CHEN G R. Avoiding congestion in cluster consensus of the second-order nonlinear multiagent systems[J]. IEEE Trans. on Neural Networks and Learning Systems, 2018, 29 (8): 3490- 3498. doi: 10.1109/TNNLS.2017.2726354
27	REN Y H, ZHOU W N, LI Z W, et al. Prescribed-time cluster lag consensus control for second-order non-linear leader-following multiagent systems[J]. ISA Transactions, 2021, 109, 49- 60. doi: 10.1016/j.isatra.2020.09.012
28	ARTSTEIN Z. Linear systems with delayed controls: a reduction[J]. IEEE Trans. on Automatic Control, 1982, 27 (4): 869- 879. doi: 10.1109/TAC.1982.1103023
29	YE H W, LI M, YANG C H, et al. Finite-time stabilization of the double integrator subject to input saturation and input delay[J]. IEEE/CAA Journal of Automatica Sinica, 2018, 5 (5): 1017- 1024. doi: 10.1109/JAS.2018.7511177
30	NI J K, LIU L, LIU C X, et al. Fixed-time leader-following consensus for second-order multi-agent systems with input delay[J]. IEEE Trans. on Industrial Electronics, 2017, 64 (11): 8635- 8646. doi: 10.1109/TIE.2017.2701775
31	WANG C Y, WEN G G, PENG Z X, et al. Integral sliding-mode fixed-time consensus tracking for second-order non-linear and time delay multi-agent systems[J]. Journal of the Franklin Institute, 2019, 356 (6): 3692- 3710. doi: 10.1016/j.jfranklin.2019.01.047

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