基于梯度估计的多智能体系统有限时间分布式优化  

Gradient estimations based distributed finite-time optimization for multi-agent systems

作　　者：朱文博 王庆领[1] ZHU Wen-bo;WANG Qing-ling(School of Automation,Southeast University,Nanjing Jiangsu 210018,China)

机构地区：[1]东南大学自动化学院,江苏南京210018

出　　处：《控制理论与应用》2023年第4期615-623,共9页Control Theory & Applications

基　　金：国家自然科学基金项目(62111530149,61973074)资助。

摘　　要：现有多智能体系统分布式优化算法大多具有渐近收敛速度,且要求系统的网络拓扑图为无向图或有向平衡图,在实际应用中具有一定的保守性.本文研究了具有强连通拓扑的多智能体系统有限时间分布式优化问题.首先,基于非光滑分析和Lyapunov稳定性理论设计了一个有限时间分布式梯度估计器.然后,基于该梯度估计器提出了一种适用于强连通有向图的有限时间分布式优化算法,实现了多智能体系统中智能体的状态在有限时间内一致收敛到全局最优状态值.与现有的有限时间分布式优化算法相比,新提出的有限时间优化算法适用于具有强连通拓扑的多智能体系统,放宽了系统对网络拓扑结构的要求.此外,本文基于Nussbaum函数方法对上述优化算法进行了拓展解决了含有未知高频增益符号的多智能体系统分布式优化问题.最后,通过仿真实例对提出的分布式优化算法的有效性进行了验证.Most of the existing distributed optimization algorithms for multi-agent systems(MASs)have asymptotic convergence,and the graphs of MASs are required to be undirected or weight balanced,which are conservative in practical application.Therefore,the distributed finite-time optimization problems for MASs which have strongly connected digraphs are investigated in this paper.First,based on the non-smooth analysis and the Lyapunov stability theory,a distributed finitetime gradient estimator is designed,then the gradient estimator based distributed finite-time optimization algorithms are proposed.With the proposed distributed optimization algorithms,the states of all agents can achieve consensus at global optimal point within finite-time.Compared with the most existing distributed finite-time optimization algorithms,the new proposed algorithms which could be deployed to the MASs with strongly connected digraphs relax the requirements of communication topologies.Moreover,the proposed algorithms are extended to solve the optimization problems in the MASs with unknown high-frequency gain signs by using the Nussbaum function based method.Finally,the simulations are conducted to verify the effectiveness of the proposed distributed optimization algorithms.

关 键 词：多智能体系统 分布式优化 有限时间 强连通有向图 非光滑分析 凸优化 

分 类 号：O224[理学—运筹学与控制论] O157.5[理学—数学]