具有量测和通信时延的随机极值搜索分布式优化  

Distributed optimization with measurement and communicationdelays via stochastic extremum seeking

作　　者：张佩佩 刘淑君[1] ZHANG Pei-Pei;LIU Shu-Jun(School of Mathematics,Sichuan University,Chengdu 610065,China;School of Data and Computer Science,Shandong Women´s University,Jinan 250300,China)

机构地区：[1]四川大学数学学院,成都610065 [2]山东女子学院数据科学与计算机学院,济南250300

出　　处：《四川大学学报(自然科学版)》2025年第2期309-324,共16页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省自然科学基金(2024NSFSC0437)。

摘　　要：针对同时存在量测和通信时延的分布式优化问题,本文基于局部目标函数的时延量测信息设计了一种基于随机极值搜索的分布式优化方法.为了分析方法的收敛性,本文对一类具有随机扰动和多个时延的非线性系统给出了随机平均定理,利用给出的随机平均定理证明方法在几乎必然的意义下指数收敛,并给出了收敛下可允许的通信时延上界.数值仿真验证了方法的有效性.In this paper,we propose a distributed algorithm based on stochastic extremum seeking to solve the distributed optimization problem in the presence of measurement and communication delays.Firstly,based on delayed measurements of local objective functions,we design a distributed algorithm via the stochastic extremum seeking method.Then,a stochastic averaging theorem for nonlinear systems with stochastic perturbation and multiple delays is established to analyze the convergence of the algorithm.Furthermore,by utilizing the established stochastic averaging theorem,we prove that the proposed algorithm is exponentially convergent in the almost sure sense and derive an upper bound on communication delays for the convergence of the algorithm.Numerical simulations are conducted to validate the effectiveness of the proposed algorithm.

关 键 词：分布式优化 随机极值搜索 随机平均 时延 

分 类 号：O231.3[理学—运筹学与控制论]