Asymptotical stability of continuous-time probabilistic logic networks based on transition rate  

作　　者：Zhitao LI Yuqian GUO Weihua GUI 

机构地区：[1]School of Automation,Central South University,Changsha 410083,China

出　　处：《Science China(Information Sciences)》2023年第3期200-209,共10页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61873284,61321003).

摘　　要：The evolution of the probability distribution for a continuous-time probabilistic logic network(CT-PLN)is determined by its transition rate matrix(TRM),which is a constant matrix that can be identified from the observed data.In the literature,the asymptotical stability criterion of a CT-PLN is expressed by using the transition probability matrix of discretization under a specific sampling period.In this paper,we derive several improved criteria that are directly expressed in terms of the TRM.We prove that a CT-PLN is asymptotically stable with respect to a given set if and only if the largest invariant subset(LIS)in the set is non-empty and the complementary set of the LIS contains no invariant subset.Thus,the asymptotical stability of a CT-PLN can be verified by applying the existing LIS algorithm twice.In addition,the condition that the complementary set of the LIS contains no invariant subset can be replaced by one of the more easily verifiable conditions,namely,the reachability condition and the rank condition.The reachability condition states that the LIS is reachable from every state outside,and the rank condition states that the complementary sub-matrix of the TRM with respect to the LIS is of full rank.For a CT-PLN being not asymptotically stable,a method of determining the domain of attraction is proposed.Finally,examples are provided to demonstrate the advantages of the proposed method.

关 键 词：asymptotical stability continuous-time probabilistic logic network semi-tensor product of matrices set stability 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]