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Contracted product of hypermatrices via STP of matrices

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Control Theory and Technology 2023年第3期21卷 265-280页

作者： daizhan cheng Min Meng Xiao Zhang Zhengping Ji Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Control Science and Engineering School of Electronics and Information EngineeringTongji UniversityShanghai 201210China National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100149China

An equivalent definition of hypermatrices is introduced.The matrix expression of hypermatrices is proposed.Using permu-tation matrices,the conversion between different matrix expressions is revealed.The various kinds of contracted products of hypermatrices are realized by semi-tensor products(STP)of matrices via matrix expressions of hypermatrices.

关键词： d-hypermatrix Matrix expression Permutation matrices-Contracted product Semi-tensor product(STP)

Survey on applications of algebraic state space theory of logical systems to finite state machines

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Science China(Information Sciences) 2023年第1期66卷 5-24页

作者： Yongyi YAN daizhan cheng Jun-E FENG Haitao LI Jumei YUE College of Information Engineering Henan University of Science and Technology Institute of Systems Science Chinese Academy of Sciences School of Mathematics Shandong University School of Mathematics and Statistics Shandong Normal University College of Agricultural Equipment Engineering Henan University of Science and Technology

Algebraic state space theory(ASST) of logical systems, developed based on the semi-tensor product(STP) which is a new matrix analysis tool built in recent ten years, provides an algebraic analysis approach for many fields of science, such as logical dynamical systems, finite-valued systems, discrete event dynamic systems, and networked game systems. This study focuses on comprehensively surveying the applications of the ASST method to the field of finite state machines(FSMs). Some necessary preliminaries on the method are first reviewed. Then the applications of the method in the FSM field are reviewed, including deterministic FSMs, nondeterministic FSMs, probabilistic FSMs, networked FSMs, and controlled and combined FSMs. In addition, other applications related to both STP and FSMs are surveyed, such as the application of FSM to Boolean control networks and the application of graph theory to FSMs. Finally, some potential research directions with respect to the ASST method in the FSM field are predicted.

关键词： Boolean control network Boolean network finite state machine learning system semi-tensor product (STP) ASST

Optimization via game theoretic control

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National Science Review 2020年第7期7卷 1120-1122页

作者： daizhan cheng Zequn Liu Key Laboratory of Systems and Control Academy of Mathematics and Systems Sciences Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

Using game theoretic control to solve optimization problem is a recently developed promising method. The key technique is to convert a networked system into a potential game, with a pre-assigned criterion as the poten... 详细信息

关键词： Game theory

Dynamics and stability for a class of evolutionary games with time delays in strategies

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Science China(Information Sciences) 2016年第9期59卷 198-207页

作者： Yuanhua WANG daizhan cheng School of Control Science and Engineering Shandong University College of Physics and Electronic Engineering Qilu Normal University

This paper investigates the modeling and stability of a class of finite evolutionary games with time delays in strategies. First, the evolutionary dynamics of a sequence of strategy profiles, named as the profile trajectory, is proposed to describe the strategy updating process of the evolutionary games with time delays.Using the semi-tensor product of matrices, the profile trajectory dynamics with two kinds of time delays are converted into their algebraic forms respectively. Then a sufficient condition is obtained to assure the stability of the delayed evolutionary potential games at a pure Nash equilibrium.

关键词： evolutionary game time delays potential game semi-tensor product of matrices stability

A new semi-tensor product of matrices

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Control Theory and Technology 2019年第1期17卷 4-12页

作者： daizhan cheng Zequn LIU The Key Laboratory of Systems and Control Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing 700790 China University of Chinese Academy of Sciences Beijing 100049 China

A new matrix product, called the second semi-tensor product (STP-Ⅱ) of matrices is proposed. It is similar to the classical semi-tensor product (STP-I). First, its fundamental properties are presented. Then, the equivalence relation caused by STP-II is obtained. Using this equivalence, a quotient space is also obtained. Finally, the vector space structure, the metric and the metric topology, the projection and subspaces, etc. of the quotient space are investigated in detail.

关键词： Second sime-tensor product (STP-Ⅱ) equivalence class quotient space topology metric

STABILIZATION OF SWITCHED LINEAR SYSTEMS WITH CONSTRAINED INPUTS

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Journal of Systems Science & Complexity 2012年第1期25卷 60-70页

作者： Wei NI daizhan cheng Department of Mathematics School of ScienceNanchang University Key Laboratory of Systems and Control Institute of Systems ScienceChinese Academy of Sciences

有抑制输入(SLSCI ) 的交换线性系统的稳定被考虑。作者设计可被考虑的线性州的反馈和有一最小的居住时间(MDT ) 到的切换的规则稳定了系统。首先为有抑制输入的每个分系统，稳定线性州的反馈和靠近环的系统的一个不变的集合同时被构造... 详细信息

有抑制输入(SLSCI ) 的交换线性系统的稳定被考虑。作者设计可被考虑的线性州的反馈和有一最小的居住时间(MDT ) 到的切换的规则稳定了系统。首先为有抑制输入的每个分系统，稳定线性州的反馈和靠近环的系统的一个不变的集合同时被构造，以便如果这设定并且仅当靠近环的系统状态在内躺着，输入限制满足。由为每个靠近环的分系统构造一个二次的 Lyapunov 函数，然后， MDT 被推出，基于 MDT 的切换策略被介绍保证交换系统的稳定性。

关键词：线性切换系统约束输入线性状态反馈 Lyapunov 镇定稳定系统闭环系统 MDT

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Matrix expression of Shapley values and its application to distributed resource allocation

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Science China(Information Sciences) 2019年第2期62卷 46-56页

作者： Yuanhua WANG daizhan cheng Xiyu LIU School of Management Science and Engineering Shandong Normal University Academy of Mathematics and Systems Science Chinese Academy of Sciences

The symmetric and weighted Shapley values for cooperative n-person games are studied. Using the semi-tensor product of matrices, it is first shown that a characteristic function can be expressed as a pseudo-Boolean function. Then, two simple matrix formulas are obtained for calculating the symmetric and weighted Shapley values. Finally, using these new formulas, a design technique for the agents’ payoff functions in distributed resource allocation problems is proposed. It is possible to design payoff functions with the weighted Shapley value by the nonsymmetric weights defined on the players, thus ensuring that the optimal allocation is a pure Nash equilibrium. Practical examples are presented to illustrate the theoretical results.

关键词： semi-tensor product of matrices Shapley value matrix formula distributed resource allocation

Profile-dynamic based fictitious play

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Science China(Information Sciences) 2021年第6期64卷 230-232页

作者： Xiao ZHANG daizhan cheng School of Control Science and Engineering Shandong University Academy of Mathematics and Systems Science Chinese Academy of Sciences

Dear editor,The fictitious play(FP) was initially proposed by Brown [1]in 1951 as a handy learning rule. The main idea of FP can be described as follows: In a game process, the player who adopts FP assumes that the others choose their strategies randomly and independently, according to a fixed distribution. Based on this assumption, the player tends to choose his or her own strategy empirically to counter the opponents and ultimately earn more benefits. Many distinguished studies have been springing up after the introduction of FP.

关键词： Profile-dynamic based fictitious play profile

Finite element approach to continuous potential games

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Science China(Information Sciences) 2021年第4期64卷 223-225页

作者： Yaqi HAO daizhan cheng School of Management Science and Engineering Shandong Normal University Academy of Mathematics and Systems Science Chinese Academy of Sciences

Dear editor,The concept of potential games was proposed for the first time by Rosenthal in 1973 [1]. The seminal study by Monderer and Shapley [2] presented systematic investigation and fundamental results for this kind of games. Some of its recent developments can be found in [3]. Because of some nice properties, potential games have been applied to many control and optimization problems, for instance the existence of Nash equilibria [4] and game theoretic control [5].

关键词： Continuous potential game finite element approach finite potential sub-game numerical solution convergence