一阶一致性收敛速率的拓扑优化方法综述  

An overview of topology optimization for improving the convergence rate of first-order consensus protocols

作　　者：陈新庄 郭志伟[1] 李江荣 CHEN Xinzhuang;GUO Zhiwei;LI Jiangrong(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000;School of Mathematics and Statistics,Northwestern Polyt Echnical University,Xi’an 710072,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000 [2]西北工业大学数学与统计学院,陕西西安710072

出　　处：《延安大学学报（自然科学版）》2022年第2期42-51,共10页Journal of Yan'an University：Natural Science Edition

基　　金：国家自然科学基金项目(61763045);陕西省自然科学基础研究计划项目(2020JM-552);延安大学博士科研启动项目(YDBK2021-03);延安大学专项科研计划项目(YDY2020-25)。

摘　　要：针对通信拓扑为无向图的一阶多智能体系统,深入探讨了提高一致性协议收敛速率的拓扑优化方法。在连续模式、周期采样模式和事件触发模式的一致性协议下,一阶多智能体系统的一致性收敛速率均由网络拓扑的代数连通度(拉普拉斯矩阵的第二小特征值)决定:通信拓扑的代数连通度越大,系统达到一致性的收敛速率越高。因此,提高一致性收敛速率的问题转化为给定拓扑的代数连通度最大化问题。目前,网络拓扑代数连通度的优化方法可归纳为数学规划方法和边或边权值的调整方法。数学规划方法将问题建模为非凸的优化模型,利用优化算法进行求解,网络规模不大时,得到近似全局最优的拓扑;边或权值调整方法主要有加边、边旋转和边交换等图操作,基于这些图操作设计贪婪算法,通常能快速得到局部最优的拓扑。基于这些方法的总结,提出了多智能体系统拓扑优化可进一步研究的若干问题。For first-order MASs with an undirected graph as its communication topology,topology optimization methods for improving the convergence rate are investigated thoroughly.Under consensus protocols,i.e.,continuous,sampled-data and event-based frameworks,the convergence rate of first-order MASs is determined by the algebraic connectivity,which shows that the larger the algebraic connectivity is,the higher the convergence rate can be achieved.Therefore,the problem of improving the convergence rate of a given MAS is modeled as the problem of maximizing the algebraic connectivity of the topology.Currently,there are two types of methods of maximizing the algebraic connectivity.One is the mathematical planning method,which models the problem as a nonconvex optimization problem that can be solved by using optimization algorithms.It can obtain an approximate global optimal topology when the network scale is small.The other method is the adjustments on edges or weights of edges by using graph operations,such as edge addition,edge rotation and edge swapping,etc.Based on these graph operations,greedy algorithms are designed and a small amount of adjustments is made to edges or weights at each iteration.This type of method can obtain a locally optimal topology with less computational cost.Based on the review of these methods,several problems that need further research are proposed for the topology optimization of MASs.

关 键 词：多智能体系统 一致性问题 收敛速率 代数连通度 网络拓扑优化 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置] O151.21[自动化与计算机技术—控制科学与工程] O157.6[理学—数学]