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Journal of Systems Science & Complexity 2022年第5期35卷 1808-1823页

作者： FAN Naqi ZHANG Lijun ZHANG Shenggui LIU Jiuqiang College of Intelligent Systems Science and Engineering Harbin Engineering UniversityHarbin 150001China School of Marine Technology Northwestern Polytechnical UniversityXi'an 710072China School of Mathematics and Statistics Northwestern Polytechnical UniversityXi'an 710129China College of Big Data Statistics Guizhou University of Finance and EconomicsGuiyang 550025China

In 2011,Liu,et *** the structural controllability of directed *** proved that the minimum number of input signals,driver nodes,can be determined by seeking a maximum matching in the directed ***,the algorithm for seeking a maximum matching is the key to solving the structural controllability problem of directed *** this study,the authors provide algebraic expressions for matchings and maximum matchings proposed by Liu,et al.(2011)via a new matrix product called semi-tensor product,based on which the corresponding algorithms are established to seek matchings and maximum matchings in digraphs,which make determining the number of driver nodes tractable in *** addition,according to the proposed algorithm,the authors also construct an algorithm to distinguish critical arcs,redundant arcs and ordinary arcs of the directed network,which plays an important role in studying the robust control *** example of a small network from Liu’s paper is used for algorithm verification.

关键词： Digraph directed network maximum matching semi-tensor product of matrices structural controllability

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Modeling and analysis of colored petri net based on the semi-tensor product of matrices

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Science China(Information Sciences) 2018年第1期61卷 70-85页

作者： Jiantao ZHAO Zengqiang CHEN Zhongxin LIU College of Computer and Control Engineering Nankai University Key Laboratory of Intelligent Robotics of Tianjin Nankai University

This paper applies the model petri net method based on the semi-tensor product of matrices to colored petri net. Firstly, we establish the marking evolution equation for colored petri net by using the semitensor product of matrices. Then we define the concept of controllability and the control-marking adjacency matrix for colored petri net. Based on the marking evolution equation and control-marking adjacency matrix, we give the necessary and sufficient condition of reachability and controllability for colored petri net. The algorithm to verify the reachability of colored petri net is given, and we analyze the computational complexity of the algorithm. Finally, an example is given to illustrate the effectiveness of the proposed theory. The significance of the paper lies in the application of the model petri net method based on the semitensor product of matrices to colored petri net. This is a convenient way of verifying whether one marking is reachable from another one as well as finding all firing sequences between any two reachable ***, the method lays the foundations for the analysis of other properties of colored petri net.

关键词： colored petri net reachability controllability marking evolution equation semi-tensor product of matrices

Leader-Follower Consensus of Multi-Agent Systems over Finite Fields via semi-tensor product of matrices

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Leader-Follower Consensus of Multi-Agent Systems over Finite...

第36届中国控制会议

作者： LI Yalu LI Haitao DING Xueying School of Mathematics and Statistics Shandong Normal University

ISBN: (纸本)9781538629185

This paper investigates the leader-follower consensus problem of multi-agent systems with time-delay over finite fields by using the semi-tensor product of ***,the dynamics of leader-follower multi-agent systems with time-delay is converted into an equivalent algebraic ***,based on the algebraic form,a necessary and sufficient condition is presented for the leader-follower consensus problem of multi-agent systems with time-delay over finite ***,based on the analysis of leader-follower multi-agent systems with time-delay,we add a control into system and present a necessary and sufficient condition for the leader-follower consensus problem of multi-agent systems with time-delay over finite fields.

关键词： Leader-Follower Consensus Distributed Control Time-Delay Finite Field semi-tensor product of matrices

Finite Input and Given Time Critical Observabilities of Finite State Machines Based on the semi-tensor product of matrices

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Finite Input and Given Time Critical Observabilities of Fini...

第40届中国控制会议

作者： He Deng Yongyi Yan Jumei Yue College of Information Engineering Henan University of Science and Technology College of Agricultural Equipment Engineering Henan University of Science and Technology

The notion of safety in safety-critical applications can be represented by the concept of critical observability. The traditional concept of critical observability refers to possibility of detecting if the current state of a nondeterministic finite state machine（NFSM）belongs to a so-called critical set for any input and any initial state. In practice, the input is always of finite length and we may only care about the state of an FSM at a given time step or the inverse problem that how to find all possible inputs moving the FSM to a critical state of interest. Thus, we propose two new concepts about critical observability, critical observability with finite input and critical observability at a given time step, to cope with these two cases. From the view of algebraic model resulting from the theory of semi-tensor product（STP）, we propose corresponding algebraic criteria and algorithms. They are based on matrix operation, which means that they naturally avoid the design of critical observers and can be solved efficiently by computers.

关键词： Logical systems logical networks finite-valued systems finite state machines critical observability semi-tensor product of matrices

Updated Formulas for semi-tensor product of matrices

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Updated Formulas for Semi-tensor Product of Matrices

第36届中国控制会议

作者： Yaqi Hao Xiao Zhang Daizhan Cheng School of Control Science and Engineering Shandong University Academy of Mathematics and Systems Science Chinese Academy of Sciences

ISBN: (纸本)9781538629185

Some main formulas about semi-tensor product（STP） of matrices are presented in their mostly updated forms. The formulas consist of（i） fundamental formulas about STP;（ii） swap and permutation related formulas;（iii） formulas for the application of STP to logical systems;（iv） the relationship of STP with Kronecker products;（v） formulas for the application of STP to game theory. The paper provides a convenient tool for investigating and applying STP.

关键词： semi-tensor product of matrices semi-tensor addition Logical system Algebraic state space representation Symmetric game

H∞ Control of Switched Homogeneous Nonlinear Systems——semi-tensor product of matrices Method

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H∞ Control of Switched Homogeneous Nonlinear Systems——Sem...

第二十九届中国控制会议

作者： ZHANG Lijun,ZHANG Kuize College of Automation,Harbin Engineering University,Harbin 150001,P.R.China

This paper investigates the problems of L2 stability and H∞control problem of a class switched homogeneous nonlinear system via the semi-tensor product（STP）of matrices ***,a homogeneous Lyapunov-like function in the form of STP is *** on this,the system in question is limited on to the unit sphere to be investigated,a switching law is designed to make sure that the normal system that is globally asymptotically stable is globally L2 stable *** the former Lyapunov-like function and the designed switching law,the H∞control problem of the considered system is reduced into a Riccati-like one via the STP of matrices method,thus a control law similar to that of linear system is designed.

关键词： Switched Homogeneous Nonlinear System L2 Stability H∞Control semi-tensor product of matrices

semi-tensor product approach for partially symmetric games

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Journal of Control and Decision 2024年第1期11卷 98-106页

作者： Lei Wang Jiandong Zhu School of Mathematical Sciences Nanjing Normal UniversityNanjingPeople’s Republic of China

In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product *** dimension and the basis of the linear subspace composed of all the PSGs with respect to a given set of partial players are *** testing equations with the minimum number are concretely determined,and the computational complexity is ***,two examples are displayed to show the theoretical results.

关键词： Partially symmetric game semi-tensor product of matrices adjacent transpositions

On equivalence of state-based potential games

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Science China(Information Sciences) 2024年第6期67卷 313-327页

作者： Han WU Jinhuan WANG Institute of Mathematics School of ScienceHebei University of Technology

In this paper, we explore state-based potential games using the semi-tensor product of ***, applying the potential equation, we derive both a necessary and sufficient condition as well as a sufficient condition to verify whether a state-based game qualifies as a potential game. Next, we present two static equivalence conditions of state-based potential games. We then delve into dynamic equivalence. We propose a criterion that allows us to identify state-based games that are dynamically equivalent to state-based potential games and share similar dynamic properties. Ultimately, we introduce the concept of state-based networked evolutionary games. We provide a necessary and sufficient condition to ensure that a state-based networked evolutionary game can be classified as a state-based potential game.

关键词： semi-tensor product of matrices state-based potential game verification equivalence state-based networked evolutionary game

Self-Triggered Set Stabilization of Boolean Control Networks and Its Applications

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IEEE/CAA Journal of Automatica Sinica 2024年第7期11卷 1631-1642页

作者： Rong Zhao Jun-e Feng Dawei Zhang the School of Mathematics Shandong UniversityShandong UniversityJinan 250100China

Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.

关键词： Boolean control networks(BCNs) output regulation self-triggered control semi-tensor product of matrices set stabilization synchronization

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A semi-tensor product Based All Solutions Boolean Satisfiability Solver

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Journal of Computer Science & Technology 2023年第3期38卷 702-713页

作者：潘鸿洋储飞 Faculty of Electrical Engineering and Computer Science Ningbo UniversityNingbo 315211China

Boolean satisfiability (SAT) is widely used as a solver engine in electronic design automation (EDA). Typically, SAT is used to determine whether one or more groups of variables can be combined to form a true formula. All solutions SAT (AllSAT) is a variant of the SAT problem. In the fields of formal verification and pattern generation, AllSAT is particularly useful because it efficiently enumerates all possible solutions. In this paper, a semi-tensor product (STP) based AllSAT solver is proposed. The solver can solve instances described in both the conjunctive normal form (CNF) and circuit form. The implementation of our method differs from incremental enumeration because we do not add blocking conditions for existing solutions, but rather compute the matrices to obtain all the solutions in one pass. Additionally, the logical matrices support a variety of logic operations. Results from experiments with MCNC benchmarks using CNF-based and circuit-based forms show that our method can accelerate CPU time by 8.1x (238x maximum) and 19.9x (72x maximum), respectively.

关键词： all solutions Boolean satisfiability(AllSAT) semi-tensor product of matrices conjunctive normal form(CNF)satisfiability circuit satisfiability