Output Tracking of Boolean Control Networks With Impulsive Effects

Li, Yiliang; Li, Jinjin; Feng, Jun‐e

doi:10.1109/access.2020.3020124

Cited by 5 publications

(2 citation statements)

References 44 publications

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“…Here, the matrix product refers to the Kronecker product. anks to the left MM STP, a Boolean network can be converted into a linear discrete-time form, which stimulates the development of Boolean networks [2][3][4]. In addition, the left MM STP also plays an important role in finite game [5][6][7], fuzzy systems [8,9], and graph theory [10,11].…”

Section: Introductionmentioning

confidence: 99%

Algebraic Relations among Four Types of Right Semi-Tensor Product

Chen

Lin

2021

Mathematical Problems in Engineering

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In this paper, algebraic relations among four kinds of right semi-tensor product (STP) are discussed. Firstly, this paper provides definitions of right STPs, consisting of the first right matrix-matrix STP, the second right matrix-matrix STP, the first right matrix-vector STP, and the second right matrix-vector STP. Secondly, relations among these right STPs are proposed. Finally, the main results show the convertibility of these right STPs.

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Section: Introductionmentioning

confidence: 99%

Algebraic Relations among Four Types of Right Semi-Tensor Product

Chen

Lin

2021

Mathematical Problems in Engineering

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“…Under the framework of Cheng product, the logical forms of BNs (BCNs) can be converted into linear (bilinear) discrete-time dynamic algebraic forms. Based on these, various remarkable issues of BNs and BCNs have been studied, to mention just a few, controllability [21,19], observability [14] [23], [36], stability and stabilization [8], [16], [44], synchronization [28], [2], disturbance decoupling [45], [35], output tracking [41], [20] and optimal control [38], [32], etc. In addition, Cheng product can also be applied to game theory [39], finite automata [43], nonlinear shift registers [26] and so on.…”

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confidence: 99%

Pinning detectability of Boolean control networks with injection mode

Feng

Wang

2022

DCDS-S

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<p style='text-indent:20px;'>This technical note presents analytical investigations on detectability of Boolean network with pinning control and injection mode (BNPCIM). Detectability represents the property to uniquely determine the current state of the system according to known input-output sequences. Using Cheng product of matrices, BNPCIM can be converted into a special algebraic form of BCNs with mix-valued logical control. Based on different research requirements, three types of detectability for BNPCIM are proposed: weak detectability, detectability and strong detectability. Under free and networked input conditions, a sequence of matrices are constructed to reflect output and state information by explicit forms. Then by using the established matrices, several necessary and sufficient conditions for three types of detectability are derived. Moreover, to avoid unnecessary calculations, the maximum steps to achieve different detectability are gained. Finally, two illustrative examples are given to demonstrate the effectiveness of the obtained results.</p>

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Stabilization of Periodic Switched k-Valued Logical Networks

2021

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The stabilization of periodic switched k-valued logical networks is investigated in this paper, and some new results are presented. The system considered consists of several k valued logical networks and these networks run in a periodic switching law. First, by using the Cheng product of matrices, a periodic switched k-valued logical (control) network is transformed into a discrete dynamic system which is written as an algebraic form. Second, the switching-state space and the switching-input-state space are defined. Then combining with the algebraic form, some necessary and sufficient conditions for the stability and the stabilization are obtained. An algorithm to find the input sequence that stabilizes the system is also provided. Finally, illustrative examples are given to support the proposed new results.

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Output Tracking of Boolean Control Networks With Impulsive Effects

Cited by 5 publications

References 44 publications

Algebraic Relations among Four Types of Right Semi-Tensor Product

Algebraic Relations among Four Types of Right Semi-Tensor Product

Pinning detectability of Boolean control networks with injection mode

Stabilization of Periodic Switched k-Valued Logical Networks

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