An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems

Wu, Yuhu; Shen, Tielong

doi:10.1016/j.sysconle.2015.04.007

Cited by 113 publications

(34 citation statements)

References 25 publications

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“…Hence we can omit the symbol mostly. This method has been widely used to study the logical dynamic systems [5,8,12,13,15,20], and game theory [6,9], etc. Next we give some properties of STP used in this paper.…”

Section: It Is Briefly Denoted Asmentioning

confidence: 99%

On coset weighted potential game

Wang

Cheng

2020

Journal of the Franklin Institute

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In this paper we first define a new kind of potential games, called coset weighted potential game, which is a generalized form of weighted potential game. Using semi-tensor product of matrices, an algebraic method is provided to verify whether a finite game is a coset weighted potential game, and a simple formula is obtained to calculate the corresponding potential function. Then some properties of coset weighted potential games are revealed. Finally, by resorting to the vector space structure of finite games, a new orthogonal decomposition based on coset weights is proposed, the corresponding geometric and algebraic expressions of all the subspaces are given by providing their bases.

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Section: It Is Briefly Denoted Asmentioning

confidence: 99%

On coset weighted potential game

Wang

Cheng

2020

Journal of the Franklin Institute

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“…This is witnessed by hundreds of research papers. A multitude of applications of STP include (i) logical dynamic systems [6], [18], [32]; (ii) systems biology [54], [20]; (iii) graph theory and formation control [45], [55]; (iv) circuit design and failure detection [33], [34], [9]; (v) game theory [21], [10], [11]; (vi) finite automata and symbolic dynamics [50], [57], [23]; (vii) coding and cryptography [58], [56]; (viii) fuzzy control [8], [17]; (ix) some engineering applications [49], [36]; and many other topics [7], [38], [52], [59], [60], [37]; just to name a few.…”

Section: Introductionmentioning

confidence: 99%

On equivalence of matrices

Cheng

2019

Asian Journal of Mathematics

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A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related structures and properties are investigated. Then the generalized matrix addition is also introduced, which extends the classical matrix addition to a class of two matrices with different dimensions.Motivated by STP of matrices, two kinds of equivalences of matrices (including vectors) are introduced, which are called matrix equivalence (M-equivalence) and vector equivalence (V-equivalence) respectively. The lattice structure has been established for each equivalence. Under each equivalence, the corresponding quotient space becomes a vector space. Under Mequivalence, many algebraic, geometric, and analytic structures have been posed to the quotient space, which include (i) lattice structure; (ii) inner product and norm (distance); (iii) topology; (iv) a fiber bundle structure, called the discrete bundle; (v) bundled differential manifold; (vi) bundled Lie group and Lie algebra. Under V-equivalence, vectors of different dimensions form a vector space V, and a matrix A of arbitrary dimension is considered as an operator (linear mapping) on V. When A is a bounded operator (not necessarily square but includes square matrices as a special case), the generalized characteristic function, eigenvalue and eigenvector etc. are defined.In one word, this new matrix theory overcomes the dimensional barrier in certain sense. It provides much more freedom for using matrix approach to practical problems.

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“…Especially, in the 2000s, an algebraic state space representation method was proposed by Cheng based on the semitensor product of matrices (STP) . It is worth noting that this method has been successfully applied to the analysis and control of BNs, and many essential results have been obtained on topological structure, controllability and observability, control design, and so on. Please refer to Li et al and Lu et al for some comprehensive surveys on STP and its applications.…”

Section: Introductionmentioning

confidence: 99%

Structural stability analysis of gene regulatory networks modeled by Boolean networks

Liang

Zhao

et al. 2019

Math Methods in App Sciences

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This paper studies the structural monostability and structural cycle‐stability of Boolean networks (BNs). Firstly, the structural‐equivalent Boolean networks are converted to the algebraic forms by using the semitensor product of matrices. Secondly, the concepts of structural monostability and structural cycle‐stability for Boolean networks are proposed. On the basis of the algebraic forms of structural‐equivalent Boolean networks, some necessary and sufficient conditions are presented for the structural monostability and structural cycle‐stability of Boolean networks. Finally, an illustrative example is worked out to show the effectiveness of the obtained results.

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An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems

Cited by 113 publications

References 25 publications

On coset weighted potential game

On coset weighted potential game

On equivalence of matrices

Structural stability analysis of gene regulatory networks modeled by Boolean networks

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