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Compound Product of Hypermatrices

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Journal of Systems Science & Complexity 2024年第1期37卷 169-183页

作者： cheng daizhan MENG Min ZHANG Xiao JI Zhengping 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.

The semi-tensor product(STP)of matrices is generalized to multidimensional arrays,called the compound product of *** product is first defined for three-dimensional hypermatrices with compatible orders and then extended to general *** different types of hyperdeterminants are introduced and certain properties are *** Lie groups and Lie algebras corresponding to the hypermatrix products are ***,these results are applied to dynamical systems.

关键词： Compound semi-tensor product hyperdeterminants hypereigenvalues and hypereigenvectors hypergeneral linear groups hypermatrices.

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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

The stabilization of switched linear systems with constrained inputs （SLSCI） is considered. The authors design admissible linear state feedbacks and the switching rule which has a minimal dwell time （MDT） to stabilized the system. First, for each subsystem with constrained inputs, a stabilizing linear state feedback and an invariant set of the closed-loop system are simultaneously constructed, such that the input constraints are satisfied if and only if the closed-loop system＇s states lie inside this set. Then, by constructing a quadratic Lyapunov function for each closed-loop subsystem, an MDT is deduced and an MDT-based switching strategy is presented to ensure the stability of the switched system.

关键词： Constrained inputs dwell time stabilization switched linear system.

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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 *** 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

On controllability and stabilizability of probabilistic Boolean control networks

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Science China(Information Sciences) 2014年第1期57卷 178-191页

作者： ZHAO Yin cheng daizhan Institute of Systems Science Chinese Academy of Sciences

The controllability of probabilistic Boolean control networks(PBCNs)is first *** the input-state incidence matrices of all models,we propose a reachability matrix to characterize the joint *** we prove that the joint reachability and the controllability of PBCNs are equivalent,which leads to a necessary and sufcient condition of the ***,the result of controllability is used to investigate the stability of probabilistic Boolean networks(PBNs)and the stabilization of PBCNs.A necessary and sufcient condition for the stability of PBNs is obtained *** introducing the control-fixed point of Boolean control networks(BCNs),the stability condition has finally been developed into a necessary and sufcient condition of the stabilization of *** necessary and sufcient conditions for controllability and stabilizability are based on reachability matrix,which are easily *** the two necessary and sufcient conditions are straightforward *** examples are provided from case to case to demonstrate the corresponding theoretical results.

关键词： probabilistic Boolean control network controllability stability stabilization semi-tensor product

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

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

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