逻辑系统的代数状态空间方法的基础、现状及其应用

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.

Algebraic state space approach to logical dynamic systems and its applications

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.