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Morgan＇s problem of Boolean control networks

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Control Theory and Technology 2017年第4期15卷 316-326页

作者： Shihua Fu Yuanhua Wang daizhan cheng Jiangbo Liu 1. School of Control Science and Engineering Shandong University Jinan Shandong 250061 China 2. School of Management Science and Engineering Shandong Normal University Jinan Shandong 250014 China 3. Department of Computer Science and Information Systems Bradley University Peoria IL 61625 U.S.A.

This paper investigates the Morgan＇s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is converted into an output- decomposed form by constructing a set of consistent outputfriendly subspaces, and a necessary and sufficient condition for the existence of the consistent output-friendly subspaces is obtained. Secondly, a type of state feedback controllers are designed to solve the Morgan＇s problem if it is solvable. By solving a set of matrix equations, a necessary and sufficient condition for converting an output-decomposed form to an input-output decomposed form is given, and by verifying the output controllability matrix, the solvability of Morgan＇s problem is obtained.

关键词： Boolean control network Morgan's problem regular subspace y-friendly subspace semi-tensor product ofmatrices

A conjecture on the norm of Lyapunov mapping

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控制理论与应用（英文版） 2009年第1期7卷 48-50页

作者： daizhan cheng Yahong ZHU Hongsheng QI Institute of Systems Science Chinese Academy of Sciences Beijing 100190 China Department of Mathematics Suzhou University Suzhou Jiangsu 215006 China

A conjecture that the norm of Lyapunov mapping LA equals to its restriction to the symmetric set, S, i.e., ｜｜LA｜｜ =｜｜LA｜s｜｜ was proposed in [1]. In this paper, a method for numerical testing is provided first... 详细信息

关键词： Lyapunov mapping Invariant subspace Norm

A SURVEY ON SEMI-TENSOR PRODUCT OF MATRICES

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Journal of Systems Science & Complexity 2007年第2期20卷 304-322页

作者： daizhan cheng Hongsheng QI Ancheng XUE Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields. In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively.

关键词： Abstract algebra differential geometry dynamic systems logic semi-tensor product

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

A minimum adequate set of multi-valued logic

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Control Theory and Technology 2021年第4期19卷 425-429页

作者： daizhan cheng Jun-e Feng Jianli Zhao Shihua Fu Research Center of Semi-tensor Product of Matrices:Theory and Applications Liaocheng UniversityLiaochengChina Key Laboratory of Systems and Control AMSSChinese Academy of SciencesBeijing 100190China School of Mathematics Shandong UniversityJinanChina

An adequate set of k-valued logic is provided,which contains only two *** is also proved that this adequate set is of minimum size。

关键词： k-valued logic Normal form Adequate set(ADS) Structure matrix of logical functions Semi-tensor product of matrices

STABILITY OF SWITCHED POLYNOMIAL SYSTEMS

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Journal of Systems Science & Complexity 2008年第3期21卷 362-377页

作者： Zhiqiang LI Yupeng QIAO Hongsheng QI daizhan cheng Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

This paper investigates the stability of （switched） polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a （switched） polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some sufficient conditions for the global stability of polynomial systems.

关键词： Global asymptotical stability semi-tensor product switched polynomial systems

Semi-tensor product approach to networked evolutionary games

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Control Theory and Technology 2014年第2期12卷 198-214页

作者： daizhan cheng Hongsheng QI Fehuang HE Tingting XU Hairong DONG Ins titu te of Systems Science Chinese Academy of Sciences Beijing 100190 China Institute of Astronautics Harbin Institute of Technology Harbin Heilongjiang 150080 China State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Beijing 100044 China

In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients： network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i） undirected graph for symmetric games; ii） directed graph for asymmetric games, and iii） d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games （FEGs） are discussed, which are i） two strategies and symmetric （S-2）; ii） two strategies and asymmetric （A-2）; and iii） three strategies and symmetric （S-3）. Three strategy updating rules （SUR） are introduced, which are i） Unconditional Imitation （UI）; ii） Fermi Rule（FR）; iii） Myopic Best Response Adjustment Rule （MBRA）. First, we review the fundamental evolutionary equation （FEE） and use it to construct network profile dynamics （NPD）of NEGs. To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation （FEE） of each player is discussed. Using FEEs, the network strategy profile dynamics （NSPD） is built by providing efficient algorithms. Finally, we consider three more complicated NEGs： i） NEG with different length historical information, ii） NEG with multi-species, and iii） NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.

关键词： Networked evolutionary game Fundamental evolutionary equation Strategy profile dynamics Homogeneous/heterogeneous NEG Semi-tensor product of matrices

On Dynamics and Nash Equilibriums of Networked Games

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IEEE/CAA Journal of Automatica Sinica 2014年第1期1卷 10-18页

作者： daizhan cheng Tingting Xu Fenghua He Hongsheng Qi the Institute of Systems Science Chinese Academy of Sciences the Institute of Sstronautics Harbin Institute of Technology

Networked noncooperative games are investigated,where each player(or agent) plays with all other players in its neighborhood. Assume the evolution is based on the fact that each player uses its neighbors current information to decide its next strategy. By using sub-neighborhood, the dynamics of the evolution is obtained. Then a method for calculating Nash equilibriums from mixed strategies of multi-players is *** relationship between local Nash equilibriums based on individual neighborhoods and global Nash equilibriums of overall network is revealed. Then a technique is proposed to construct Nash equilibriums of an evolutionary game from its one step static Nash equilibriums. The basic tool of this approach is the semi-tensor product of matrices, which converts strategies into logical matrices and payoffs into pseudo-Boolean functions, then networked evolutionary games become discrete time dynamic systems.

关键词： Networked non-cooperative game local infor-mation sub-neighborhood fundamental evolutionary equation Nash equilibrium

On Hamiltonian realization of time-varying nonlinear systems

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Science in China(Series F) 2007年第5期50卷 671-685页

作者： WANG YuZhen Ge S. S. cheng daizhan School of Control Science and Engineering Shandong University Jinan 250061 China Department of Electrical and Computer Engineering the National University of Singapore Singapore 117576 Institute of Systems Science Chinese Academy of Sciences Beijing 100080 China

This paper Investigates Hamiltonian realization of time-varying nonlinear （TVN） systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacooian matrix of a TVN system is nonsingular, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is sin- gular; this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a non- singular main diagonal block. Furthermore, some sufficient （necessary and sufficient） conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.

关键词： generalized Hamiltonian realization dissipative Hamiltonian realization diffoemorphism structural construction