Sampled-Data State Feedback Stabilization of Boolean Control Networks

Liu, Yang; Cao, Jinde; Sun, Liangjie; Lu, Jianquan

doi:10.1162/neco_a_00819

Cited by 70 publications

(20 citation statements)

References 37 publications

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“…Thus, one can also investigate the controllability and synchronization problems of LCNs in which there is interaction between different layers in form of (12). Thus, in this paper, we assume that there is no interaction between different layers to simplify the model.…”

Section: B Further Discussion On Model (7)mentioning

confidence: 99%

Controllability and Synchronization Analysis of Identical-Hierarchy Mixed-Valued Logical Control Networks

Zhong

Huang

et al. 2017

IEEE Trans. Cybern.

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This paper investigates the controllability and synchronization problems for identical-hierarchy mixed-valued logical control networks. The logical network considered is hierarchical, and Boolean network is a special case of logical network. Here, identical-hierarchy means that there are identical number of nodes in each layer of logical network and corresponding nodes have the same dimension for any two layers of logical networks. Meanwhile, in each layer of logical networks, the dimensions of nodes are distinct, and it is called a mixed-valued logical network. First, the controllability problem is investigated and two notions of controllability are presented, i.e., group-controllability and simultaneously-controllability. By resorting to Perron-Frobenius theorem, some necessary and sufficient criteria are obtained to guarantee group-controllability and simultaneously-controllability, respectively. Second, based on the algebraic representation of the studied model, synchronization problems are analytically discussed for two types of controls, i.e., free control sequences and state-output feedback control. Finally, two numerical examples are presented to show the validness of our main results.

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Section: B Further Discussion On Model (7)mentioning

confidence: 99%

Controllability and Synchronization Analysis of Identical-Hierarchy Mixed-Valued Logical Control Networks

Zhong

Huang

et al. 2017

IEEE Trans. Cybern.

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“…Since then, many scholars have paid increasing attention to the study of Boolean networks and many nice results have been presented on the topological structure [2][3][4][5], and on the control problem [6]. In the last two decades, Cheng and co-authors have developed a new matrices product, called the semi-tensor product [7], which has been successfully applied to study the Boolean (control) network [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], probabilistic Boolean control network [24][25][26], and some other related fields [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov‐Based Stability of Mix‐Valued Logical Networks

Zhao

Meng

Liu

2018

Asian Journal of Control

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This paper investigates Lyapunov-based stability of mix-valued logical networks. First, we consider the pseudo-logical function, and give its general logical expression. Second, based on pseudo-logical functions, we give some definitions on the strict-Lyapunov function of mix-valued logical networks and establish a necessary and sufficient condition about the stability. Third, the obtained results are applied to probabilistic logical networks, and a necessary and sufficient condition of globally stability is proposed. Finally, the study of illustrative examples shows that new results presented in this paper work very well.

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“…Extensive studies have been done on control of BNs [15,[17][18][19][20], control of complex networks with linear dynamics [21][22][23], and the chariterization of multiagent controlability from network structures [24,25]. Recently, semi-tensor product (STP) proposed in [13,18] has been used widely in various control models of BN [16,[26][27][28][29][30][31]; the stability and stabilization have also been considered as an important aspect in control of BNs [32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

On the Number of Driver Nodes for Controlling a Boolean Network to Attractors

Hou

Ruan

Ching

et al. 2018

Preprint

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It is known that many driver nodes are required to control complex biological networks. Previous studies imply that O(N ) driver nodes are required in both linear complex network and Boolean network models with N nodes if an arbitrary state is specified as the target. In this paper, we mathematically prove under a reasonable assumption that the expected number of driver nodes is only O(log 2 N + log 2 M ) for controlling Boolean networks if the targets are restricted to attractors, where M is the number of attractors. Since it is expected that M is not very large in many practical networks, this is a significant improvement. This result is based on discovery of novel relationships between control problems on Boolean networks and the coupon collector's problem, a well-known concept in combinatorics. We also provide lower bounds of the number of driver nodes as well as simulation results using artificial and realistic network data, which support our theoretical findings.

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Sampled-Data State Feedback Stabilization of Boolean Control Networks

Cited by 70 publications

References 37 publications

Controllability and Synchronization Analysis of Identical-Hierarchy Mixed-Valued Logical Control Networks

Controllability and Synchronization Analysis of Identical-Hierarchy Mixed-Valued Logical Control Networks

Lyapunov‐Based Stability of Mix‐Valued Logical Networks

On the Number of Driver Nodes for Controlling a Boolean Network to Attractors

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