引用本文:程代展,齐洪胜.逻辑系统的代数状态空间方法的基础、现状及其应用[J].控制理论与应用,2014,31(12):1632~1639.[点击复制]
CHENG Dai-Zhan,QI Hong-Sheng.Algebraic state space approach to logical dynamic systems and its applications[J].Control Theory and Technology,2014,31(12):1632~1639.[点击复制]
逻辑系统的代数状态空间方法的基础、现状及其应用
Algebraic state space approach to logical dynamic systems and its applications
摘要点击 2788  全文点击 3197  投稿时间：2014-08-23  修订日期：2014-11-02
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DOI编号  10.7641/CTA.2014.40777
  2014,31(12):1632-1639
中文关键词  矩阵半张量积  逻辑动态系统  代数状态空间方程  纯状态与混合状态  控制与博弈
英文关键词  semi-tensor product  logical dynamic systems  algebraic state space equation  pure state and mixed state  control and game
基金项目  国家自然科学基金资助项目(61273013, 61333001, 61104065).
作者单位E-mail
程代展* 中国科学院 数学与系统科学研究院 系统控制重点实验室 dcheng@iss.ac.cn 
齐洪胜 中国科学院 数学与系统科学研究院 系统控制重点实验室  
中文摘要
      逻辑系统指自变量只取有限个值的动态系统. 包括2值的经典逻辑(或布尔逻辑)、k值逻辑、(一般)有限值逻辑. 近年来, 利用矩阵半张量积发展起来的逻辑动态系统的代数状态空间方法得到长足的进展和普遍的重视. 同时, 它被广泛应用于许多工程问题或理论研究中. 它类似于Rn上由微分或差分方程描述的动态系统的Kalman状态空间方法, 为逻辑系统的分析与控制设计提供了一个便捷的平台. 本文首先对该方法作一简要介绍, 然后, 对该新兴学科分支的现状作一评述. 最后, 详细介绍该方法目前的应用以及其更广泛的应用前景.
英文摘要
      The logical dynamic system in this paper stands for the systems where the state variables can take only finite values. Particularly, when the number is 2 it is a classical logic (or Boolean logic); k-valued logic, and general finitely valued (general) logic. In recent years, using semi-tensor product of matrices the algebraic state space approach to logical dynamic systems has been developed and widely appreciated. It has been used to many engineering problems and to theoretical researches. Parallel to the Kalman state space approach to continuous state space dynamics where the differential equations or difference equations are used to describe the dynamic systems, the algebraic state space approach may provide a convenient platform for analyzing and control design of logical systems. The purpose of this paper is two fold: First, we give a brief survey on this new approach; then we introduce its current research topics and main results. Finally many applications and predict the potential of its further applications are presented.