非线性多智能体系统事件触发神经网络自适应分布式优化控制

吴畏; 李克文; 佟绍成

doi:10.16383/j.aas.c250659

非线性多智能体系统事件触发神经网络自适应分布式优化控制

doi: 10.16383/j.aas.c250659 cstr: 32138.14.j.aas.c250659

1.
辽宁工业大学理学院锦州 121001

基金项目: 国家自然科学基金(62503212, 62573216), 辽宁省兴辽英才青年拔尖人才资助计划(XLYC2503078), 辽宁省科技厅博士启动基金计划项目(2025-BS-0503), 辽宁省青年科技人才托举工程资助

详细信息

作者简介:
吴畏：辽宁工业大学理学院内聘副教授. 主要研究方向为非线性控制, 自适应控制, 非线性多智能体系统, 自适应分布式优化控制. E-mail: wuw2017@163.com

李克文：辽宁工业大学理学院副教授. 主要研究方向为预设时间控制, 优化控制, 非线性系统的模糊控制和自适应控制. E-mail: likewen2018@163.com

佟绍成：辽宁工业大学理学院教授. 主要研究方向为模糊系统理论, 智能控制, 自适应控制和优化控制. 本文通信作者. E-mail: jztongsc@163.com

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出版历程
- 收稿日期: 2025-11-18
- 录用日期: 2026-01-30
- 网络出版日期: 2026-04-03
- 刊出日期: 2026-07-20

Event-triggered Neural Network Adaptive Distributed Optimal Control for Nonlinear Multi-agent Systems

1.
College of Science, Liaoning University of Technology, Jinzhou 121001

Funds: Supported by National Natural Science Foundation of China (62503212, 62573216), Liaoning Xingliao Talent Plan for Young Top-Notch Talents (XLYC2503078), Liaoning Province Science and Technology Plan Joint Program (2025-BS-0503), and Liaoning Young Elite Scientists Sponsorship Program

More Information

Author Bio:
WU Wei　Internal associate professor at the College of Science, Liaoning University of Technology. His research interests include nonlinear control, adaptive control, nonlinear multi-agent systems, and adaptive distributed optimal control

LI Ke-Wen　Associate professor at the College of Science, Liaoning University of Technology. His research interests include prescribed-time control, optimal control, fuzzy control and adaptive control for nonlinear systems

TONG Shao-Cheng　Professor at the College of Science, Liaoning University of Technology. His research interests include fuzzy system theory, intelligent control, adaptive control, and optimal control. Corresponding author of this paper

摘要

摘要: 针对具有未知动力学的非线性多智能体系统, 研究事件触发神经网络自适应分布式优化控制问题. 通过结合神经网络与微分图博弈理论, 构建一种新型事件触发神经网络自适应分布式优化控制器. 为解决执行器频繁更新问题, 设计事件触发机制. 建立基于神经网络的强化学习算法, 学习优化控制器与哈密顿−雅可比−贝尔曼方程的解析解, 利用当前采样数据和历史存储数据设计评价网络的权重更新机制. 构造Lyapunov函数证明了被控非线性多智能体系统为渐近稳定并达到Nash均衡. 计算机仿真结果验证了所提分布式最优控制方案的有效性.
- 非线性多智能体系统 /
- 事件触发机制 /
- 分布式神经网络自适应优化控制 /
- Nash均衡
Abstract: This paper investigates the event-triggered neural network (NN) adaptive distributed optimal control problem for nonlinear multi-agent systems with unknown dynamics. By integrating NN with differential graphical game theory, a novel event-triggered NN adaptive distributed optimal controller is developed. To deal with the problem of frequent updates of the actuator, an event-triggered mechanism is designed. A reinforcement learning algorithm based on NN is designed to learn the optimal controller and the analytical solution of the Hamilton-Jacobi-Bellman equation, where the updating mechanisms for the critic network weights are designed by integrating current sampled data and historical stored data. The asymptotic stability of the controlled nonlinear multi-agent systems and the achievement of Nash equilibrium are proved via Lyapunov function. Computer simulation results demonstrate the effectiveness of the proposed distributed optimal control scheme.
- nonlinear multi-agent system /
- event-triggered mechanism /
- distributed neural network adaptive optimal control /
- Nash equilibrium

HTML全文

图 1 事件触发分布式优化控制框图

Fig. 1 The block diagram of event-triggered distributed optimal control

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图 2 网络拓扑图

Fig. 2 Network topology diagram

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图 3 跟随者输出和领导者输出的轨迹

Fig. 3 Trajectories of follower output and leader output

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图 5 分布式优化控制器的曲线

Fig. 5 The curves of distributed optimal controllers

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图 4 一致性跟踪误差的曲线

Fig. 4 The curves of consensus tracking errors

下载: 全尺寸图片幻灯片

参考文献(26)

[1]	He W L, Xu B, Han Q L, Qian F. Adaptive consensus control of linear multiagent systems with dynamic event-triggered stra-tegies. IEEE Transactions on Cybernetics, 2020, 50(7): 2996−3008 doi: 10.1109/TCYB.2019.2920093
[2]	Li Z K, Liu X D, Ren W, Xie L H. Distributed tracking control for linear multiagent systems with a leader of bounded unknown input. IEEE Transactions on Automatic Control, 2013, 58(2): 518−523 doi: 10.1109/TAC.2012.2208295
[3]	He W L, Zhang B, Han Q L, Qian F, Kurths J, Cao J D. Leader-following consensus of nonlinear multiagent systems with stochastic sampling. IEEE Transactions on Cybernetics, 2017, 47(2): 327−338
[4]	Yu W W, Wang H, Cheng F, Yu X H, Wen G H. Second-order consensus in multiagent systems via distributed sliding mode control. IEEE Transactions on Cybernetics, 2017, 47(8): 1872−1881 doi: 10.1109/TCYB.2016.2623901
[5]	Wang F, Chen B, Lin C, Li X H. Distributed adaptive neural control for stochastic nonlinear multiagent systems. IEEE Transactions on Cybernetics, 2017, 47(7): 1795−1803 doi: 10.1109/TCYB.2016.2623898
[6]	Shen Q K, Jiang B, Shi P, Zhao J. Cooperative adaptive fuzzy tracking control for networked unknown nonlinear multiagent systems with time-varying actuator faults. IEEE Transactions on Fuzzy Systems, 2014, 22(3): 494−504 doi: 10.1109/TFUZZ.2013.2260757
[7]	Chen C L P, Ren C E, Du T. Fuzzy observed-based adaptive consensus tracking control for second-order multiagent systems with heterogeneous nonlinear dynamics. IEEE Transactions on Fuzzy Systems, 2016, 24(4): 906−915 doi: 10.1109/TFUZZ.2015.2486817
[8]	Zhang J L, Zhang H G, Feng T. Distributed optimal consensus control for nonlinear multiagent system with unknown dynamic. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(8): 3339−3348 doi: 10.1109/TNNLS.2017.2728622
[9]	Su W, Mu C X, Yang X, Bian J S, Sun C Y. Optimal tracking control for leader-following consensus of nonlinear multiagent systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2025, 55(5): 3098−3107 doi: 10.1109/TSMC.2025.3539351
[10]	Qin J H, Li M, Shi Y, Ma Q C, Zheng W X. Optimal synchronization control of multiagent systems with input saturation via off-policy reinforcement learning. IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(1): 85−96 doi: 10.1109/TNNLS.2018.2832025
[11]	Wen G X, Chen C L P, Feng J, Zhou N. Optimized multi-agent formation control based on an identifier-actor-critic reinforcement learning algorithm. IEEE Transactions on Fuzzy Systems, 2018, 26(5): 2719−2731 doi: 10.1109/TFUZZ.2017.2787561
[12]	Sun J L, Liu C S. Distributed fuzzy adaptive backstepping optimal control for nonlinear multimissile guidance systems with input saturation. IEEE Transactions on Fuzzy Systems, 2019, 27(3): 447−461 doi: 10.1109/tfuzz.2018.2859904
[13]	Liu M S, Wan Y, Lopez V G, Lewis F L, Hewer G A, Estabridis K. Differential graphical game with distributed global Nash solution. IEEE Transactions on Control of Network Systems, 2021, 8(3): 1371−1382 doi: 10.1109/TCNS.2021.3065654
[14]	Qian Y Y, Liu M S, Wan Y, Lewis F L, Davoudi A. Distributed adaptive Nash equilibrium solution for differential graphical games. IEEE Transactions on Cybernetics, 2023, 53(4): 2275−2287 doi: 10.1109/TCYB.2021.3114749
[15]	Ren Y X, Wang Q S, Duan Z S. Optimal leader-following consensus control of multi-agent systems: A neural network based graphical game approach. IEEE Transactions on Network Science and Engineering, 2022, 9(5): 3590−3601 doi: 10.1109/TNSE.2022.3185019
[16]	Mazouchi M, Naghibi-Sistani M B, Sani S K H. A novel distributed optimal adaptive control algorithm for nonlinear multi-agent differential graphical games. IEEE/CAA Journal of Automatica Sinica, 2018, 5(1): 331−341 doi: 10.1109/jas.2017.7510784
[17]	Zhang Y W, Zhao B, Liu D R, Zhang S C. Distributed fault tolerant consensus control of nonlinear multiagent systems via adaptive dynamic programming. IEEE Transactions on Neural Networks and Learning Systems, 2024, 35(7): 9041−9053
[18]	Zhang H G, Zhang J L, Yang G H, Luo Y H. Leader-based optimal coordination control for the consensus problem of multiagent differential games via fuzzy adaptive dynamic programming. IEEE Transactions on Fuzzy Systems, 2015, 23(1): 152−163 doi: 10.1109/TFUZZ.2014.2310238
[19]	Wu W, Tong S C. Adaptive fuzzy distributed optimal FTC for nonlinear multiagent systems based multiplayer differential game. IEEE Transactions on Fuzzy Systems, 2025, 33(2): 657−668 doi: 10.1109/TFUZZ.2024.3488015
[20]	Long L J, Wang F L, Chen Z Y. Robust adaptive dynamic event-triggered control of switched nonlinear systems. IEEE Transactions on Automatic Control, 2023, 68(8): 4873−4887 doi: 10.1109/TAC.2022.3217100
[21]	Cao L, Yao D Y, Li H Y, Meng W, Lu R Q. Fuzzy-based dynamic event triggering formation control for nonstrict-feedback nonlinear MASs. Fuzzy Sets and Systems, 2023, 452: 1−22 doi: 10.1016/j.fss.2022.03.005
[22]	Tong S C, Zhou H D, Li Y M. Neural network event-triggered formation fault-tolerant control for nonlinear multiagent systems with actuator faults. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023, 53(12): 7571−7582 doi: 10.1109/TSMC.2023.3298656
[23]	Wei Q L, Jiao S S, Dong Q, Wang F Y. Event-triggered robust parallel optimal consensus control for multiagent systems. IEEE/CAA Journal of Automatica Sinica, 2025, 12(1): 40−53 doi: 10.1109/JAS.2024.124773
[24]	Zhang C J, Ji L H, Yang S D, Guo X, Li H Q. Distributed optimal consensus control for multiagent systems based on event-triggered and prioritized experience replay strategies. Science China Information Sciences, 2025, 68(1): Article No. 112206 doi: 10.1007/s11432-023-4183-4
[25]	Lewis F L, Jagannathan S, Yesildirak A. Neural Network Control of Robot Manipulators and Non-linear Systems. London: CRC Press, 2020.
[26]	Peng Z H, Jiang Y, Liu L, Shi Y. Path-guided model-free flocking control of unmanned surface vehicles based on concurrent learning extended state observers. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023, 53(8): 4729−4739 doi: 10.1109/TSMC.2023.3256371