电子学报2026，Vol.54Issue(3)：938-946,9.DOI:10.12263/DZXB.20251219
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
摘要
Abstract
This paper investigates a distributed time-varying optimization problem for Euler-Lagrange swarm intelli-gent systems over unbalanced directed communication topologies.Consider a swarm intelligent system composed of multi-ple 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 un-balanced communication topologies,solution drift induced by time-varying cost functions,and inherent system nonlineari-ties 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 di-rected graphs is designed.It eliminates the impact of communication topology imbalance by online estimation of the left ei-genvector 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 con-trol layer,a tracking controller with a system parameter adaptation law is designed for each agent.Utilizing the linear pa-rameterization 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 per-formance.To analyze the convergence of the proposed algorithm,first,the input-to-state stability theory is utilized to ana-lyze 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 validat-ed through numerical simulations involving ten two-link manipulators.The results demonstrate that the joint angle trajecto-ries of all agents can accurately track the optimal trajectory.关键词
分布式优化/欧拉-拉格朗日群体智能系统/非平衡有向图/时变函数/自适应控制/协同控制Key words
distributed optimization/Euler-Lagrange swarm intelligent systems/unbalanced directed graph/time-varying function/adaptive control/cooperative control分类
信息技术与安全科学引用本文复制引用
张云飞,栾萌,赵丹,黄頔,黄廷文..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(3):938-946,9.基金项目
国家自然科学基金(No.62325304,No.U2541220) （No.62325304,No.U2541220）
江苏省自然科学基金(No.BK20253020) （No.BK20253020）
浙江省"尖兵"研发攻关计划(No.2025C01055) （No.2025C01055）
江苏省应用数学科学研究中心(No.BK20233002) National Natural Science Foundation of China(No.62325304,No.U2541220) （No.BK20233002）
Basic Research Program of Jiangsu(No.BK20253020) （No.BK20253020）
Key Research and Development Program of Zhejiang Province(No.2025C01055) （No.2025C01055）
Jiangsu Provincial Scientific Research Center of Applied Mathematics(No.BK20233002) （No.BK20233002）
