山东师范大学学报(自然科学版)

2019, v.34;No.148(04) 379-392

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有限值动态系统的分析与控制研究进展
RECENT DEVELOPMENT ON ANALYSIS AND CONTROL OF FINITE-VALUE DYNAMIC SYSTEMS

李海涛;李雅璐;王淑玲;刘玉娜;
Li Haitao;Li Yalu;Wang Shuling;Liu Yuna;School of Mathematics and Statistics, Shandong Normal University;

摘要(Abstract):

介绍了近期关于有限值动态系统及其应用的一些研究结果,包括有限值动态系统的背景、常见的有限值动态系统、有限值动态系统分析与控制的重要研究工作等.主要介绍了逻辑动态系统、网络演化博弈、有限域网络和非线性反馈移位寄存器四种有限值动态系统.针对四种有限值动态系统,分别介绍了基本研究问题和当前热点研究问题,比如:逻辑动态系统的集合能控、依分布稳定、镇定,有限域网络的一致性、主从一致性等.主要对基于矩阵半张量积方法研究有限值动态系统的最新研究结果进行综合概述.最终给出了有限值动态系统现存的问题以及研究前景.
This paper presents a comprehensive survey on recent developments of finite-value dynamic system and its applications, including the background of finite-value dynamic system, some branches of finite-value dynamic systems, and some fundamental results and current works on finite-value systems. Particularly, some fundamental results and current remarkable works on logical dynamic systems, networked evolutionary games, finite-field networks, and nonlinear feedback shift registers are summarized, such as set controllability, stability in distribution, and stabilization of logical dynamic systems, consensus and leader-follower consensus of finite-field networks, and so on. The main concern of this survey is to present a detailed introduction to recent developments on finite-value dynamic systems under the framework of semi-tensor product of matrices. Finally, the paper presents some existing problems and research prospects of finite-value dynamic systems.

关键词(KeyWords): 有限值动态系统;逻辑动态系统;网络演化博弈;有限域网络;移位寄存器;矩阵半张量积
finite-value dynamic system;logical dynamical systems;networked evolutionary games;finite-field networks;shift register;semi-tensor product of matrices

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基金项目(Foundation): 国家自然科学基金资助项目(61503225,61873150);; 山东省自然科学杰出青年基金资助项目(JQ201613)

作者(Author): 李海涛;李雅璐;王淑玲;刘玉娜;
Li Haitao;Li Yalu;Wang Shuling;Liu Yuna;School of Mathematics and Statistics, Shandong Normal University;

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