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The structure of canalizing functions

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控制理论与应用（英文版） 2010年第3期8卷 375-381页

作者： Zhiqiang LI daizhan cheng Department of Mathematics and Information Science Henan University of Economics and Law Zhengzhou Henan 450002 China Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

The structure of a canalizing function is discussed. Using a new matrix product, namely semitensor product, the logical function is expressed in its matrix form. From its matrix expression, a criterion is obtained to test whether a logical function is a canalizing function. Then a formula is obtained to calculate the number of canalizing functions. Moreover, an algorithm is presented to generate canalizing functions. Finally, some results obtained are extended to seminested canalizing functions.

关键词： Canalizing function Boolean function Seminested canalizing function

From STP to game-based control

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Science China(Information Sciences) 2018年第1期61卷 9-27页

作者： daizhan cheng Hongsheng QI Zequn LIU Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of Sciences University of Chinese Academy of Sciences

This paper provides a comprehensive survey on semi-tensor product(STP) of matrices and its applications to different disciplines. First of all, the STP and its basic properties are introduced. Meanwhile, its inside physical meaning is explained. Second, its application to conventional dynamic systems is presented. As an example, the region of attraction of stable equilibriums is discussed. Third, its application to logical systems is presented. Particularly, the algebraic state space representation of logical systems and the important role it plays in analysis and control of logical systems are emphasized. Fourth, its application to finite games is discussed. The most interesting problems include potential game, evolutionary game, and game theoretic control. Finally, the mathematical essence of STP is briefly introduced.

关键词： semi-tensor product of matrices Boolean network logical(control) system finite game game theoretic control

Advances in automation and control research in China

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Science in China(Series F) 2009年第11期52卷 1954-1963页

作者： cheng daizhan Key Laboratory of Systems and Control Academy of Mathematics & Systems Science Chinese Academy of Sciences Beijing 100190 China

Automation is the utilization of control techniques together with other information technology to control industrial processes, reducing the need for human intervention. It plays a highly important role in social and economy as well as in daily life. Control theory is the theory of automation, and is an interdisciplinary branch of engineering and mathematics, examining the behavior of dynamical systems. China has a long history of manufacturing automatic devices. In recent years, some rapid progresses in control theory have been made in China. Many new theories and new methodologies have been developed to meet the increasing demands in industry, agriculture, defense, and other social sectors. Contemporary sciences such as complexity, systems biology, quantum technologies, have also found their close links to control theories and technologies. On the other hand, control theory itself has many unsolved fundamental problems requiring further studies and investigation. This paper is to review the development and progress that have been made in all these aspects in China. Some remarks on the future development of control theory are also presented.

关键词： control theory high tech oriented contemporary sciences fundamental problems

A Comprehensive Survey on STP Approach to Finite Games

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Journal of Systems Science & Complexity 2021年第5期34卷 1666-1680页

作者： cheng daizhan WU Yuhu ZHAO Guodong FU Shihua Key Laboratory of Systems and Control Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijing 100190China. Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education Dalian University of TechnologyDalian 116081China School of Mathematics and Statistics Shandong Normal UniversityJinan 250014China. School of Mathematical Sciences Liaocheng UniversityLiaocheng 252000China

Nowadays the semi-tensor product(STP)approach to finite games has become a promising new *** paper provides a comprehensive survey on this prosperous *** a brief introduction for STP and finite(networked)games,a description for the principle and fundamental technique of STP approach to finite games is *** several problems and recent results about theory and applications of finite games via STP are presented.A brief comment about the potential use of STP to artificial intelligence is also proposed.

关键词： Finite game game-theoretic control potential game semi-tensor product vector space structure of finite game

Logic and logic-based control

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控制理论与应用（英文版） 2008年第1期6卷 26-36页

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

This paper gives a matrix expression of logic. Under the matrix expression, a general description of the logical operators is proposed. Using the semi-tensor product of matrices, the proofs of logical equivalences, implications, etc., can be simplified a lot. Certain general properties are revealed. Then, based on matrix expression, the logical operators are extended to multi-valued logic, which provides a foundation for fuzzy logical inference. Finally, we propose a new type of logic, called mix-valued logic, and a new design technique, called logic-based fuzzy control. They provide a numerically computable framework for the application of fuzzy logic for the control of fuzzy systems.

关键词： Semi-tensor product Matrix expression of logic Mix-valued logic Logic-based fuzzy control

Symmetry-based decomposition of finite games

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Science China(Information Sciences) 2019年第1期62卷 164-176页

作者： Changxi LI Fenghua HE Ting LIU daizhan cheng School of Astronautics Harbin Institute of Technology Key Laboratory of Systems and Control Academy of Mathematics and Systems SciencesChinese Academy of Sciences

The symmetry-based decompositions of finite games are investigated. First, the vector space of finite games is decomposed into a symmetric subspace and an orthogonal complement of the symmetric subspace. The bases of the symmetric subspace and those of its orthogonal complement are ***, the potential-based orthogonal decompositions of two-player symmetric/antisymmetric games are presented. The bases and dimensions of all dual decomposed subspaces are revealed. Finally, some properties of these decomposed subspaces are obtained.

关键词： potential game symmetric game decomposition Nash equilibrium semi-tensor product of matrices

Vector Space Structure of Finite Evolutionary Games and Its Application to Strategy Profile Convergence

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Journal of Systems Science & Complexity 2016年第3期29卷 602-628页

作者： QI Hongsheng WANG Yuanhua LIU Ting cheng daizhan Key Laboratory of Systems and Control Institute of Systems ScienceChinese Academy of Sciences School of Control Science and Engineering Shandong University

A vector space structure is proposed for the set of finite games with fixed nmnbers of players and strategies for each players. Two statical equivalences are used to reduce tile dimension of finite games. Under the vector space structure the subspaces of exact and weighted potential games are investigated. Formulas are provided to calculate them. Then the finite evolutionary games （EGs） are considered. Strategy profile dynamics is obtained using different strategy updating rules （SURs）. Certain SURs, which assure the convergence of trajectories to pure Nash equilibriums, are investigated. Using the vector space structure, the projection of finite games to the subspace of exact （or weighted） potential games is considered, and a simple formula is given to calculate the projection. The convergence of near potential games to an c-equilibrium is studied. Further more, the Lyapunov function of EGs is defined and its application to the convergence of EGs is presented. Finally, the near potential function for an EG is defined, and it is proved that if the near potential function of an EG is a Lyapunov function, the EG will converge to a pure Nash equilibrium. Some examples are presented to illustrate the results.

关键词： Evolutionary game Lyapunov function Nash equilibrium near potential ihmction potential.

A survey on potential evolutionary game and its applications

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Journal of Control and Decision 2015年第1期2卷 26-45页

作者： daizhan cheng Yuanhua Wang Ting Liu Key Laboratory of Systems&Control Institute of Systems ScienceAcademy of Mathematics&Systems ScienceChinese Academy of SciencesBeijingP.R.China School of Control Science and Engineering Shandong UniversityJinanP.R.China

Basic concepts about the finite potential games and the networked evolutionary games(NEGs)are *** new developments are surveyed,including(i)formulas for verifying whether a finite game is(weighted)potential and for calculating the(weighted)potential function;and(ii)the fundamental network equation and strategy profile dynamics of *** some applications are introduced,which include:(i)convergence of NEGs;(ii)congestion control;(iii)distributed coverage of graphs.

关键词： potential function Networked Evolutionary Game convergence congestion control distributed coverage of graphs semi-tensor product of matrices

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 *** matrix expression of hypermatrices is *** permu-tation matrices,the conversion between different matrix expressions is *** various kinds of contracted products of hyper... 详细信息

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