非平衡有向图下欧拉-拉格朗日群体智能系统分布式时变优化

张云飞; 栾萌; 赵丹; 黄頔; 黄廷文

doi:10.12263/DZXB.20251219

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非平衡有向图下欧拉-拉格朗日群体智能系统分布式时变优化

信息丰富时代的群体智能理论与技术 | 更新时间：2026-06-26

- 非平衡有向图下欧拉-拉格朗日群体智能系统分布式时变优化
- Distributed Time-Varying Optimization for Euler-Lagrange Swarm Intelligent Systems over Unbalanced Directed Graphs
- 电子学报 2026年54卷第3期页码：938-946
- 作者机构：
  
  1.辽宁工程技术大学理学院，辽宁阜新 123032
  2.岭南大学数据科学学院，香港特别行政区
  3.东南大学自动化学院，江苏南京 210096
  4.湖北珞珈实验室，湖北武汉 430072
  5.深圳理工大学计算机科学与控制工程学院，广东深圳 518107
- 作者简介：
  
  张云飞男，1998年出生于江苏省宿迁市。现为辽宁工程技术大学硕士研究生。主要研究方向为最优化理论与应用。 E-mail: zhangyflgd@163.com
  栾萌女，1996年出生于河北省衡水市。现为岭南大学数据科学学院博士后。主要研究方向为多智能体系统的分布式优化与博弈决策。 E-mail: mengluan@ln.edu.hk
  赵丹女，1992年出生于陕西省西安市。现为东南大学自动化学院助理研究员。主要研究方向为分布式攻击隔离与弹性协同控制。 E-mail: danzhao@seu.edu.cn
  黄頔男，1989年出生于湖北省武汉市。现为湖北珞珈实验室副研究员，硕士生导师。主要研究方向为复杂系统协同控制、空天飞行器智能控制、姿态与轨道控制。 E-mail: dhuang@whu.edu.cn
  黄廷文男，1967年出生于重庆市。现为深圳理工大学计算机科学与控制工程学院教授。主要研究方向为多智能体系统、自适应控制、最优控制。 E-mail: huangtw2024@163.com
- 基金信息：
  
  国家自然科学基金(62325304;U2541220);江苏省自然科学基金(BK20253020);浙江省“尖兵”研发攻关计划(2025C01055);江苏省应用数学科学研究中心(BK20233002)
- DOI：10.12263/DZXB.20251219
  中图分类号： TP273;
- 收稿：2026-01-25，
  
  录用：2026-02-24，
  
  纸质出版：2026-03-25
- 稿件说明：
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张云飞, 栾萌, 赵丹, 等. 非平衡有向图下欧拉-拉格朗日群体智能系统分布式时变优化[J]. 电子学报, 2026, 54(03): 938-946.

ZHANG Yunfei, LUAN Meng, ZHAO Dan, et al. Distributed Time-Varying Optimization for Euler-Lagrange Swarm Intelligent Systems over Unbalanced Directed Graphs[J]. Acta Electronica Sinica, 2026, 54(03): 938-946.
张云飞, 栾萌, 赵丹, 等. 非平衡有向图下欧拉-拉格朗日群体智能系统分布式时变优化[J]. 电子学报, 2026, 54(03): 938-946. DOI：10.12263/DZXB.20251219

ZHANG Yunfei, LUAN Meng, ZHAO Dan, et al. Distributed Time-Varying Optimization for Euler-Lagrange Swarm Intelligent Systems over Unbalanced Directed Graphs[J]. Acta Electronica Sinica, 2026, 54(03): 938-946. DOI：10.12263/DZXB.20251219

摘要

本文研究非平衡有向通信图下欧拉-拉格朗日群体智能系统的分布式时变优化问题。考虑由多个具有欧拉-拉格朗日动力学的智能体组成的群体智能系统，其信息交互建模为强连通且非平衡的有向图，每个智能体拥有私有的局部时变代价函数，目标是为每个智能体设计控制输入，使所有智能体实时状态达成一致并共同收敛至全局代价函数的时变最优解。实际应用中，通信拓扑非平衡导致的加权一致性偏差、时变代价函数引起的解漂移，与系统固有的非线性及参数不确定性交织耦合，为设计分布式优化算法带来了严峻的理论挑战。为克服上述挑战，本文提出一种融合分布式优化器与自适应控制器的新型双层算法框架。在优化层，设计了一种适用于非平衡有向图的分布式优化器，通过在线估计拉普拉斯矩阵零特征值对应的左特征向量以消除通信拓扑的非平衡性影响，同时引入时变梯度补偿器以动态修正最优轨迹漂移，生成参考速度信号。在控制层，针对每个智能体设计了基于系统参数自适应律的跟踪控制器，利用欧拉-拉格朗日系统的线性参数化性质在线更新未知参数估计值，使智能体的实际速度能够精确跟踪参考速度，从而抑制模型不确定性对跟踪性能的影响。为分析算法的收敛性，首先，利用输入-状态稳定性理论分析优化器的动态演化，证明当跟踪误差有界且收敛时智能体状态能够达成一致；其次，构造Lyapunov函数分析最优跟踪步骤，结合Barbalat引理证明全局梯度之和渐近趋于零；基于此，严格证明了当控制器参数满足给定的不等式条件时，所有智能体的实时状态全局渐近收敛于时变最优轨迹；最后，通过包含十个双连杆机械臂的数值仿真验证了所提算法的有效性，仿真结果表明所有智能体的关节角度轨迹均能快速、准确地跟踪最优轨迹。

Abstract

This paper investigates a distributed time-varying optimization problem for Euler-Lagrange swarm intelligent systems over unbalanced directed communication topologies. Consider a swarm intelligent system composed of multiple agents with Euler-Lagrange dynamics

where information exchange is modeled as a strongly connected and unbalanced directed graph

and each agent possesses its own private local time-varying cost function. The objective is to design control inputs for each agent such that all agents’ real-time states achieve consensus and collectively converge to the time-varying optimal solution of the global cost function. In practical applications

the coupling of weighted consensus bias caused by unbalanced communication topologies

solution drift induced by time-varying cost functions

and inherent system nonlinearities and parameter uncertainties presents severe theoretical challenges for the design of distributed optimization algorithms. To overcome the aforementioned challenges

this paper proposes a novel dual-layer algorithm framework that integrates a distributed optimizer and an adaptive controller. In the optimization layer

a distributed optimizer tailored for unbalanced directed graphs is designed. It eliminates the impact of communication topology imbalance by online estimation of the left eigenvector associated with the zero eigenvalue of the Laplacian matrix

while introducing a time-varying gradient prediction compensation term to dynamically correct the optimal trajectory drift

thus generating a reference velocity signal. In the control layer

a tracking controller with a system parameter adaptation law is designed for each agent. Utilizing the linear parameterization property of Euler-Lagrange systems

it updates estimates of unknown parameters online

enabling the agents’ actual velocities to accurately track the reference velocity

thus mitigating the impact of model uncertainties on tracking performance. To analyze the convergence of the proposed algorithm

first

the input-to-state stability theory is utilized to analyze the optimizer dynamics

demonstrating that the states of agents achieve consensus when the tracking error is bounded and convergent. Second

a Lyapunov function is constructed to analyze the optimal tracking step

and Barbalat’s lemma is applied to prove that the sum of global gradients asymptotically approaches zero. Consequently

it is rigorously proven that the real-time states of all agents globally and asymptotically converge to the time-varying optimal trajectory provided the controller parameters satisfy the certain inequality conditions. Finally

the effectiveness of the proposed algorithm is validated through numerical simulations involving ten two-link manipulators. The results demonstrate that the joint angle trajectories of all agents can accurately track the optimal trajectory.

关键词

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references

江碧涛 , 温广辉 , 周佳玲 , 等 . 智能无人集群系统跨域协同技术研究现状与展望 [J ] . 中国工程科学 , 2024 , 26 ( 1 ): 117 - 126 . DOI: 10.15302/j-sscae-2024.01.015 http://dx.doi.org/10.15302/j-sscae-2024.01.015

Jiang Bitao , Wen Guanghui , Zhou Jialing , et al . Cross-domain cooperative technology of intelligent unmanned swarm systems: Current status and prospects [J ] . Strategic Study of CAE , 2024 , 26 ( 1 ): 117 - 126 . (in Chinese) . DOI: 10.15302/j-sscae-2024.01.015 http://dx.doi.org/10.15302/j-sscae-2024.01.015

雷兴明 , 邢昌风 , 吴玲 , 等 . 基于分布式约束优化的多平台导弹协同航路规划 [J ] . 电子学报 , 2012 , 40 ( 10 ): 2068 - 2072 . DOI: 10.3969/j.issn.0372-2112.2012.10.027 http://dx.doi.org/10.3969/j.issn.0372-2112.2012.10.027

Lei Xingming , Xing Changfeng , Wu Ling , et al . Path planning for multi-platform missiles based on distributed constrained optimization [J ] . Acta Electronica Sinica , 2012 , 40 ( 10 ): 2068 - 2072 . (in Chinese) . DOI: 10.3969/j.issn.0372-2112.2012.10.027 http://dx.doi.org/10.3969/j.issn.0372-2112.2012.10.027

温广辉 , 余星火 , 黄廷文 , 等 . 模型参数不确定下多无人艇系统固定时间二分编队跟踪控制 [J ] . 自动化学报 , 2025 , 51 ( 3 ): 669 - 677 .

Wen Guanghui , Yu Xinghuo , Huang Tingwen , et al . Fixed-time bipartite formation tracking control for multi-USV systems with uncertain model parameters [J ] . Acta Automatica Sinica , 2025 , 51 ( 3 ): 669 - 677 . (in Chinese)

Olfati-Saber R , Murray R M . Consensus problems in networks of agents with switching topology and time-delays [J ] . IEEE Transactions on Automatic Control , 2004 , 49 ( 9 ): 1520 - 1533 . DOI: 10.1109/tac.2004.834113 http://dx.doi.org/10.1109/tac.2004.834113

Spong M W , Hutchinson S , Vidyasagar M . Robot modeling and control [M ] . Hoboken : John Wiley & Sons , 2006 .

饶凌风 , 耿娜 , 张勇 , 等 . 不确定环境下无人机任务分配的种群交互式粒子群算法 [J ] . 电子学报 , 2025 , 53 ( 8 ): 2678 - 2690 .

Rao Lingfeng , Geng Na , Zhang Yong , et al . Population interactive particle swarm optimization algorithm for UAV task allocation in uncertain environments [J ] . Acta Electronica Sinica , 2025 , 53 ( 8 ): 2678 - 2690 . (in Chinese)

蒋伟进 , 杜熙晨 , 蒋意容 , 等 . 基于自适应联邦学习的环境监测群智感知算法 [J ] . 电子学报 , 2025 , 53 ( 3 ): 821 - 835 .

Jiang Weijin , Du Xichen , Jiang Yirong , et al . Adaptive federated learning based crowd sensing algorithm for environmental monitoring [J ] . Acta Electronica Sinica , 2025 , 53 ( 3 ): 821 - 835 . (in Chinese)

朱旭 , 闫建国 , 屈耀红 . 高阶多智能体系统的一致性分析 [J ] . 电子学报 , 2012 , 40 ( 12 ): 2466 - 2471 .

Zhu Xu , Yan Jianguo , Qu Yaohong . Consensus analysis for high-order multi-agent systems [J ] . Acta Electronica Sinica , 2012 , 40 ( 12 ): 2466 - 2471 . (in Chinese)

Zhang Yanqiong , Deng Zhenhua , Hong Yiguang . Distributed optimal coordination for multiple heterogeneous Euler-Lagrangian systems [J ] . Automatica , 2017 , 79 : 207 - 213 . DOI: 10.1016/j.automatica.2017.01.004 http://dx.doi.org/10.1016/j.automatica.2017.01.004

Zou Yao , Meng Ziyang , Hong Yiguang . Adaptive distributed optimization algorithms for Euler-Lagrange systems [J ] . Automatica , 2020 , 119 : 109060 . DOI: 10.1016/j.automatica.2020.109060 http://dx.doi.org/10.1016/j.automatica.2020.109060

Zou Yao , Huang Bomin , Meng Ziyang . Distributed continuous-time algorithm for constrained optimization of networked Euler-Lagrange systems [J ] . IEEE Transactions on Control of Network Systems , 2021 , 8 ( 2 ): 1034 - 1042 . DOI: 10.1109/tcns.2021.3068352 http://dx.doi.org/10.1109/tcns.2021.3068352

Qin Zhengyan , Jiang Liangze , Liu Tengfei , et al . Distributed optimization for uncertain Euler-Lagrange systems with local and relative measurements [J ] . Automatica , 2022 , 139 : 110113 . DOI: 10.1016/j.automatica.2021.110113 http://dx.doi.org/10.1016/j.automatica.2021.110113

Ding Yong , Wang Hanlei , Ren Wei . Distributed continuous-time optimization for networked Lagrangian systems with time-varying cost functions under fixed graphs [C ] // 2022 American Control Conference (ACC) . Piscataway : IEEE , 2022 : 2779 - 2784 . DOI: 10.23919/acc53348.2022.9867341 http://dx.doi.org/10.23919/acc53348.2022.9867341

Ding Yong , Wang Hanlei , Ren Wei . Distributed continuous-time time-varying optimization for networked Lagrangian systems with quadratic cost functions [J ] . Automatica , 2025 , 171 : 111882 . DOI: 10.1016/j.automatica.2024.111882 http://dx.doi.org/10.1016/j.automatica.2024.111882

Luan Meng , Wen Guanghui , Liu Hongzhe , et al . Distributed discrete-time convex optimization with closed convex set constraints: Linearly convergent algorithm design [J ] . IEEE Transactions on Cybernetics , 2024 , 54 ( 4 ): 2271 - 2283 . DOI: 10.1109/tcyb.2023.3270185 http://dx.doi.org/10.1109/tcyb.2023.3270185

Luan Meng , Wen Guanghui , Lyu Yuezu , et al . Distributed constrained optimization over unbalanced time-varying digraphs: A randomized constraint solving algorithm [J ] . IEEE Transactions on Automatic Control , 2024 , 69 ( 8 ): 5154 - 5167 . DOI: 10.1109/tac.2023.3347328 http://dx.doi.org/10.1109/tac.2023.3347328

Wen Guanghui , Zheng Weixing , Wan Ying . Distributed robust optimization for networked agent systems with unknown nonlinearities [J ] . IEEE Transactions on Automatic Control , 2023 , 68 ( 9 ): 5230 - 5244 . DOI: 10.1109/tac.2022.3216965 http://dx.doi.org/10.1109/tac.2022.3216965

Li Zhenhong , Ding Zhengtao , Sun Junyong , et al . Distributed adaptive convex optimization on directed graphs via continuous-time algorithms [J ] . IEEE Transactions on Automatic Control , 2018 , 63 ( 5 ): 1434 - 1441 . DOI: 10.1109/tac.2017.2750103 http://dx.doi.org/10.1109/tac.2017.2750103

Wen Guanghui , Duan Zhisheng , Yu Wenwu , et al . Consensus in multi-agent systems with communication constraints [J ] . International Journal of Robust and Nonlinear Control , 2012 , 22 ( 2 ): 170 - 182 . DOI: 10.1002/rnc.1687 http://dx.doi.org/10.1002/rnc.1687

Simonetto A , Mokhtari A , Koppel A , et al . A class of prediction-correction methods for time-varying convex optimization [J ] . IEEE Transactions on Signal Processing , 2016 , 64 ( 17 ): 4576 - 4591 . DOI: 10.1109/tsp.2016.2568161 http://dx.doi.org/10.1109/tsp.2016.2568161

Rahili S , Ren Wei . Distributed continuous-time convex optimization with time-varying cost functions [J ] . IEEE Transactions on Automatic Control , 2017 , 62 ( 4 ): 1590 - 1605 . DOI: 10.1109/tac.2016.2593899 http://dx.doi.org/10.1109/tac.2016.2593899

Huang Bomin , Zou Yao , Meng Ziyang , et al . Distributed time-varying convex optimization for a class of nonlinear multiagent systems [J ] . IEEE Transactions on Automatic Control , 2020 , 65 ( 2 ): 801 - 808 . DOI: 10.1109/tac.2019.2917023 http://dx.doi.org/10.1109/tac.2019.2917023

Khalil H K . Nonlinear systems [M ] . 3rd ed . Upper Saddle River : Prentice Hall , 2002 .

Slotine J J , Li Weiping . Applied nonlinear control [M ] . Englewood Cliffs : Prentice Hal , 1991 .

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