Event-Triggered Control for the Stabilization of Probabilistic Boolean Control Networks

Zhu, Shiyong; Lou, Jungang; Liu, Yang; Li, Yuanyuan; Wang, Zhen

doi:10.1155/2018/9259348

Cited by 39 publications

(16 citation statements)

References 43 publications

(71 reference statements)

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“…Based on this, a BN (or BCN) can be converted into the corresponding algebraic form by calculating its unique transition matrix. Therefore, many fundamental and interesting problems have been investigated for BNs and BCNs, such as the controllability [5,6], stabilization [7][8][9][10][11][12][13][14][15], observability [16][17][18][19], disturbance decoupling problem [20] synchronization [21], function perturbations [22], optimal control [23][24][25][26], normalization problem [27], and others. The STP has also been widely applied in games [28,29] and asynchronous sequential machines [30,31].…”

Section: Introductionmentioning

confidence: 99%

Robust Invariant Set Analysis of Boolean Networks

Lou

Liu

et al. 2019

Complexity

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In this paper, the robust invariant set (RIS) of Boolean (control) networks with disturbances is investigated. First, for a given fixed point, consider a special set called immediate neighborhoods of the fixed point; then a discrete derivative of Boolean functions at the fixed point is used to analyze the robust invariance, based on which a sufficient condition is obtained. Second, for more general sets, the robust output control invariant set (ROCIS) of Boolean control networks (BCNs) is investigated by semitensor product (STP) of matrices. Then, under a given output feedback controller, we obtain a necessary and sufficient condition to check whether a given set is robust control invariant set (RCIS). Furthermore, output feedback controllers are designed to make a set to be a RCIS. Finally, the proposed methods are illustrated by a reduced model of the lac operon in E. coli.

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Section: Introductionmentioning

confidence: 99%

Robust Invariant Set Analysis of Boolean Networks

Lou

Liu

et al. 2019

Complexity

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“…From the viewpoint of network reliability, network model is generally classified as binary state network model and multistate network model [10]. Binary state network model assumes two states for network components: fully working or completely failed [17][18][19][20]. For example, in a gene regulatory network, the state of each gene is described by two levels: either active (fully working) or inactive (completely failed) [20], so it can be modeled as a binary state network.…”

Section: Introductionmentioning

confidence: 99%

“…Binary state network model assumes two states for network components: fully working or completely failed [17][18][19][20]. For example, in a gene regulatory network, the state of each gene is described by two levels: either active (fully working) or inactive (completely failed) [20], so it can be modeled as a binary state network. However, a number of actual complex systems are often affected by various random parameters due to external or internal uncertainties [21], such that they could exhibit multiple behaviors.…”

Section: Introductionmentioning

confidence: 99%

Efficient Enumeration of d-Minimal Paths in Reliability Evaluation of Multistate Networks

Niu

2019

Complexity

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A number of real-world complex networks can be modeled as multistate networks for performance analysis. A multistate network consists of multistate components and possesses multiple different performance levels. For such a network, reliability is concerned with the probability of the network capacity level greater than or equal to a predetermined demand level d. One major method for multistate network reliability evaluation is using d-minimal paths. This paper proposes an efficient algorithm to find d-minimal paths. First, a new concept of qualified state vector is defined so as to fix a relatively smaller search space of d-minimal paths, and a sufficient and necessary condition for a qualified state vector to be d-minimal path is established. Then, the max-flow algorithm and the enumeration algorithm are integrated to search for d-minimal paths in the determined search space that is recursively divided into subspaces such that the searching efficiency can be increased as much as possible. Both analytical and numerical results show that the proposed algorithm is more efficient in finding all d-minimal paths. In addition, a case study related to power transmission network is performed to demonstrate the implication of network reliability.

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“…Two survey papers survey recent advances in event-triggered communication and control has been published recently [30,31]. ere were also a number of works concerning the event-triggered control for the synchronization control problem, which can be found in [32][33][34][35][36][37][38][39] and references there in.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Complex Dynamical Networks with Hybrid Time Delay under Event-Triggered Control: The Threshold Function Method

2019

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This paper investigates the synchronization of general complex dynamical networks (CDNs) with both internal delay and transmission delay. Event-triggered mechanism is applied for the feedback controllers, in which the triggered function is formed as a nonincreasing function. Both continuous feedback and sampled-data feedback methods are studied. According to Lyapunov stability theorem and generalized Halanay’s inequality, quasi-synchronization criteria are derived at first. The synchronization error is bounded with some parameters of the triggered function. Then, the completed synchronization can be guaranteed as a special case. Finally, coupled neural networks as numerical simulation examples are given to verify the theoretical results.

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Event-Triggered Control for the Stabilization of Probabilistic Boolean Control Networks

Cited by 39 publications

References 43 publications

Robust Invariant Set Analysis of Boolean Networks

Robust Invariant Set Analysis of Boolean Networks

Efficient Enumeration of d-Minimal Paths in Reliability Evaluation of Multistate Networks

Synchronization of Complex Dynamical Networks with Hybrid Time Delay under Event-Triggered Control: The Threshold Function Method

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