布尔控制网络关于任意输入的能达性、能观性和能检性  

Reachability, Observability and Detectability of Boolean Control Networks W.R.T. Arbitrary Inputs

作　　者：李一峰 周雪丽 刘云杰 LI Yifeng;ZHOU Xueli;LIU Yunjie(National Center for Applied Mathematics in Chongqing,Chongqing 401331;School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China)

机构地区：[1]重庆国家应用数学中心,重庆401331 [2]南京师范大学数学科学学院,南京210023

出　　处：《重庆师范大学学报（自然科学版）》2023年第4期6-14,共9页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市自然科学基金项目(No.CSTB2022NSCQ-MSX0325);重庆市教育委员会科学技术研究项目(No.KJQN202200524);重庆师范大学博士启动基金人才引进项目(No.21XLB045);重庆市科学技术局项目(No.ncamc2022-msxm05)。

摘　　要：在矩阵半张量积理论框架下,研究布尔控制网络关于任意输入的能达性、能观性和能检性问题。首先研究在任意输入下布尔控制网络的能达性,提出任意输入下的能达性和集能达性定义,并构造检验系统在任意输入下能达(集能达)的能达性矩阵(集能达性矩阵)。其次,应用任意输入下集能达性的研究结果,研究布尔控制网络在任意输入下的能观性和能检性问题,获得这两个问题可解的充分必要条件。最后,给出两个例子验证所得理论结果的有效性。The reachability,observability,and detectability w.r.t.arbitrary inputs of Boolean control networks(BCNs)are investigated via the semi-tensor product of matrices.The reachability w.r.t.arbitrary inputs of BCNs is studied.The definitions of the reachability and set reachability w.r.t.arbitrary inputs are proposed,and the reachability matrix and set reachability matrix w.r.t.arbitrary inputs are constructed to check the reachability and set reachability of BCNs.As applications of the set reachability w.r.t.arbitrary inputs,the observability and detectability with arbitrary inputs of BCNs are then studied.Necessary and sufficient conditions for the observability and detectability w.r.t.arbitrary inputs of BCNs are obtained.Finally,numerical examples are given to illustrate the obtained theoretical results.

关 键 词：能达性 能观性 能检性 布尔控制网络 任意输入 

分 类 号：O233[理学—运筹学与控制论]