欧拉–拉格朗日系统在权重不平衡有向图下的分布式优化算法
Distributed Optimization Algorithm for Euler-Lagrange Systems over Weight-Unbalanced Digraph
DOI: 10.12677/aam.2024.137306, PDF,    国家自然科学基金支持
作者: 石 佳, 高彩霞：内蒙古大学数学科学学院，内蒙古 呼和浩特 收稿日期：2024年6月15日；录用日期：2024年7月9日；发布日期：2024年7月17日
关键词: 分布式优化算法；权重不平衡有向图；欧拉–拉格朗日系统；Distributed Optimization； Weight-Unbalanced Digraph； Euler-Lagrange Systems
摘要: 本文研究了欧拉–拉格朗日(EL)多智能体系统在权重不平衡有向图下的分布式优化问题，优化目标为通过智能体间的局部通讯最小化全局目标函数，该目标函数为智能体自身局部目标函数的和。为解决该问题，本文设计平衡补偿变量调节拓扑权重，并提出EL系统在权重不平衡有向图下的分布式优化算法，该算法使智能体状态达成一致的同时，协同最小化全局目标函数。最后，给出一个基于Simulink的数值仿真验证所提出算法的有效性。
Abstract: This paper investigates the distributed optimization problem of Euler-Lagrange (EL) multi-agent systems in weighted unbalanced digraphs, the optimization objective of this paper is to minimize the global cost function through local communications among agents, where the global cost function is summed up by local ones assigned to corresponding agent. To address this problem, the balanced compensation variables are designed to adjust the topology weights, then, a distributed optimization algorithm for EL systems over weight-unbalanced digraphs is proposed, which enables agents to achieve consensus while cooperatively minimizing the global cost function. Finally, numerical simulations based on Simulink are provided to verify the effectiveness of the proposed algorithm.
文章引用：石佳, 高彩霞. 欧拉–拉格朗日系统在权重不平衡有向图下的分布式优化算法[J]. 应用数学进展, 2024, 13(7): 3201-3211. https://doi.org/10.12677/aam.2024.137306

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