The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)，The Natural Science Foundation of Shandong Province
布尔网络可以简洁有效地描述作用在有限集上的动态离散模型. 然而, 随着研究的深入以及一些实际问题的需要, 传统的布尔网络已经不能满足建模的需求, 由此衍生出多值逻辑网络以及混合值逻辑网络, 统称为有限值动态系统. 通过矩阵半张量积, 有限值动态系统可以转化为便于处理的等价代数形式. 本文对矩阵半张量积以及有限值动态系统的最新发展, 作了概括与总结. 对矩阵半张量的推广, 即各种广义的矩阵半张量积及其应用做了简单梳理. 着重总结了有限值动态系统的最新成果, 包括最新的研究问题、最新的研究方法以及最新的几种控制器设计.
Boolean network is a succinct and effective tool for describing dynamic discrete models acting on finite sets. However, with the deepening of research and the need of practical problems, traditional Boolean networks have been unable to satisfy the requirements of modeling. Therefore, multi-valued logical networks and mix-valued logical networks come into being, which are collectively referred to as finite-valued dynamic systems (FVDSs). By virtue of semi-tensor product (STP) of matrices, FVDSs can be converted into equivalent algebraic forms that are easy to deal with. This paper provides a comprehensive survey on the recent developments of STP and FVDSs. Various generalizations of STP and their applications are systematically combed. In addition, the latest achievements of FVDSs are emphatically elaborated, involving the current hot issues, the latest research methods, as well as the novel controller design schemes.