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Basis for the quotient space of matrices under equivalence

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Science China(Information Sciences) 2020年第8期63卷 248-250页

作者： Kuize ZHANG ACCESS Linnaeus Center School of Electrical Engineering and Computer ScienceKTH Royal Institute of Technology College of Automation Harbin Engineering University

Dear editor,The semi-tensor product (STP) of matrices, proposed by Cheng in 2001 [1], is a generalization of the conventional matrix product and well defined at every two finite-dimensional matrices. In2016, Cheng [2] proposed a new concept of semitensor addition (STA), which is a generalization of the conventional matrix addition and well defined at every two finite-dimensional matrices with the same ratio between the numbers of rows and

关键词： matrix equivalence basis Boolean network semitensor product semitensor addition

Matrix expression and reachability analysis of finite automata

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控制理论与应用（英文版） 2012年第2期10卷 210-215页

作者： Xiangru XU, Yiguang HONG Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this paper, we propose a matrix-based approach for finite automata and then study the reachability conditions. Both the deterministic and nondeterministic automata are expressed in matrix forms, and the necessary and sufficient conditions on reachability are given using semitensor product of matrices. Our results show that the matrix expression provides an effective computational way for the reachability analysis of finite automata.

关键词： Finite automata Reachability Matrix expression semitensor product

维普期刊数据库

Polynomial representation for orthogonal projections onto subspaces of finite games 36

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Polynomial representation for orthogonal projections onto su...

Fault detectability of Boolean control networks via nonaugmented methods

第36届中国控制会议

作者： Kuize Zhang College of Automation Harbin Engineering University Department of Electrical and Computer Engineering Technical University of Munich

ISBN: (纸本)9781538629185

The space of finite games can be decomposed into three orthogonal subspaces[2],which are the subspaces of pure potential games,nonstrategic games,and pure harmonic *** orthogonal projections onto these subspaces are represented as the Moore-Penrose inverses of the corresponding linear operators（i.e.,matrices）[2],but no closed forms for these orthogonal projections are *** this paper,in the framework of the semitensor product of matrices,we give explicit polynomial representation（actually closed forms） for these orthogonal projections.

关键词： Decomposition of finite game Potential game Nonstrategic game Harmonic game semitensor product

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Science China(Information Sciences) 2023年第12期66卷 94-106页

作者： Rong ZHAO Caixia WANG Yongyuan YU Jun-E FENG School of Mathematics Shandong University

This study is concerned with the fault detectability of Boolean control networks(BCNs) by two nonaugmented methods. Firstly, the equivalent system-based approach is considered, and the equivalence of BCNs is applied to analyze weak active fault detectability. Further, an iterative matrix set-based approach is proposed, by which, several novel criteria for strong and weak active fault detectability are ***, effective algorithms are designed to check strong and weak active fault detectability and generate all feasible input sequences with the minimum length. In comparison, our results reduce the computational complexity dramatically than the existing studies.

关键词： Boolean control network fault detectability equivalent system nonaugmented method semitensor product