随机乘性噪声约束多输出离散系统的均方可检测性  

Mean square detectability of multi-output discrete-time systems over stochastic multiplicative noise channels

作　　者：邬依林 沈志萍[2] 张瑾 WU Yi-lin;SHEN Zhi-ping;ZHANG Jin(Department of Computer Science,Guangdong University of Education,Guangzhou Guangdong 510310,China;School of Mathematics and Information Sciences,Henan Normal University,Xinxiang Henan 453007,China)

机构地区：[1]广东第二师范学院计算机科学系,广东广州510310 [2]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《控制理论与应用》2024年第8期1487-1494,共8页Control Theory & Applications

基　　金：国家自然科学基金项目(62203155);广东省自然科学基金项目(2022A1515010485);河南省科技攻关计划项目(222102240051);广东第二师范学院网络工程重点学科项目(ZD2017004);河南师范大学国家青年基金培育项目(2021PL28)资助。

摘　　要：本文主要讨论乘性噪声约束下,多输出离散系统均方可检测问题.假定子信道容量是先验固定的,不能任意分配.首先,利用乘性噪声对通信信道进行建模,基于编码/观测器协同设计思想,建立系统均方可检测动态方程.其次,根据控制不等式性质和能控性分解技术,给出网络化系统可检测的充分条件.再次,基于循环分解技术,系统最优补灵敏度以及控制不等式理论等,求得网络化系统可检测的必要条件.所给出的充分和必要条件可用开环系统拓扑熵与子信道信道容量以控制不等式形式表示.最后,数值算例及仿真验证结论的合理性.This study discusses the detectability of multiple output discrete-time systems under multiplicative noise constraints.It is assumed that the capacities of sub-channels are fixed prior and cannot be arbitrarily allocated.First,a multiplicative noise is used to model the communication channel,and the dynamic equation of the systems is established by virtue of the coding/observer co-design idea.Second,according to the properties of majorization and controllable decomposition technique,a sufficient condition for the detectability of the networked control systems(NCSs)is given.Meanwhile,based on the cyclic decomposition technique,the optimal complementary sensitivity and the majorization theory,a necessary condition for the detectability of the NCSs is also obtained.The sufficient and necessary conditions can be expressed by the form of majorization,which is composed of the topology entropy of the open loop system and the channel capacities of sub-channels.Finally,the rationality of the conclusion is verified by numerical examples and simulation.

关 键 词：离散时间控制系统 信道容量 均方可检测 控制不等式 乘性噪声 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]