矩阵半张量积方法在逻辑网络和相关系统中的应用综述  

A survey on the applications of semi-tensor product of matrices on logical networks and other related systems

作　　者：卢剑权[1] 李海涛[2] 刘洋[3] 李芳菲[4] 曹进德[1] LU Jianquan LI Haitao LIU Yang LI Fangfei CAO Jinde(School of Mathematics, Southeast University, Nanjing 210096 School of Mathematics and Statistics,Shandong Normal University, Jinan 250014 College of Mathematics, Physics and Information Engineering, Zhejiang Normal University ,Jinhua 321004 School of Science, East China University of Science and Technology, Shanghai 200237)

机构地区：[1]东南大学数学学院,南京210096 [2]山东师范大学数学与统计学院,济南250014 [3]浙江师范大学数理与信息工程学院,金华321004 [4]华东理工大学理学院,上海200237

出　　处：《南京信息工程大学学报（自然科学版）》2017年第4期341-364,共24页Journal of Nanjing University of Information Science & Technology（Natural Science Edition）

基　　金：国家自然科学基金(61573102;11671361;61374065;61403139;61503225)

摘　　要：本文介绍了近期关于逻辑网络及其应用的一些最近的结果,包括逻辑网络的背景、矩阵半张量积(STP)的新矩阵乘积的理论、逻辑网络的一些基本研究以及一些当前的重要工作.特别介绍了逻辑网络的一些基本问题,比如可控性、可观性、稳定性、镇定、同步、最优控制以及扰动解耦等.由于在处理逻辑网络问题方面具有很大的潜力和优势,STP方法被海内外很多学者关注并将其用于相关问题的研究.目前,一些新的领域被广泛研究,包括牵引控制、函数扰动、系统解耦、输出追踪、符号动力学等.本文主要对基于STP方法研究逻辑网络以及STP方法的其他相关应用进行了综述.This paper gives a survey on recent developments of logical networks and some related systems, including the background of logical networks, the theory of semi-tensor product （STP） of matrices, some fundamental works on logical networks, and some recent related works. In particular, some very recent interesting works for the past ten years are presented, concerning the topics of controllability, observability, stability and stabilization, synchronization, optimal control, disturbance decoupling, and so on. Since the method of STP has great potential in dealing with logical networks and some other related systems, a great attraction from domestic and oversea researchers has been paid on the study of STP and its applications.Some recent important research areas are also surveyed in this paper including pinning control, function perturbations, system decomposition, output tracking issues, symbolic dynamics, and so on.The main objective is to give a comprehensive introduction to the application of STP on logical networks and some other systems.

关 键 词：矩阵半张量积 逻辑网络 布尔网络 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]