Lebesgue sampling control of gene regulatory networks with stochastic disturbance: a Boolean network approach

Dongshan Fu; Xiao Wang; Feng Lu; Dongshan Fu; Xiao Wang; Feng Lu

doi:10.3934/mmc.2026001

Mathematical Modelling and Control

2026, Volume 6, Issue 1: 1-13. doi: 10.3934/mmc.2026001

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Research article

Lebesgue sampling control of gene regulatory networks with stochastic disturbance: a Boolean network approach

1.
First Clinical Medical College, Shandong University of Traditional Chinese Medicine, Jinan 250014, China
2.
School of Mathematical Science, Liaocheng University, Liaocheng 252000, China

Received: 15 July 2025 Revised: 03 September 2025 Accepted: 29 September 2025 Published: 27 February 2026

The dynamic behavior and regulatory mechanisms of gene regulatory networks (GRNs) have attracted considerable attention in systems biology, as they play a crucial role in elucidating the principles of gene regulation, cellular evolution, and the pathogenesis of complex diseases. GRNs are widely modeled as Boolean networks (BNs) due to their intuitive logic, descriptive simplicity, and computational efficiency. In this paper, a robust set stabilization Lebesgue sampling control method was studied. First, a criterion was proposed to verify the robust set stabilization of BNs, and an algorithm was developed to design the sampled data state feedback controls (SDSFCs) within a given Lebesgue sampling region. Second, an improved sampling region was designed using the truth matrix method to reduce control update frequency while maintaining stability. Finally, the effectiveness of the proposed method was validated through a reduced model of the lac operon in Escherichia coli.
- gene regulatory networks,
- Lebesgue sampling,
- robust set stabilization,
- stochastic disturbances,
- semi-tensor product
Citation: Dongshan Fu, Xiao Wang, Feng Lu. Lebesgue sampling control of gene regulatory networks with stochastic disturbance: a Boolean network approach[J]. Mathematical Modelling and Control, 2026, 6(1): 1-13. doi: 10.3934/mmc.2026001

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Abstract

The dynamic behavior and regulatory mechanisms of gene regulatory networks (GRNs) have attracted considerable attention in systems biology, as they play a crucial role in elucidating the principles of gene regulation, cellular evolution, and the pathogenesis of complex diseases. GRNs are widely modeled as Boolean networks (BNs) due to their intuitive logic, descriptive simplicity, and computational efficiency. In this paper, a robust set stabilization Lebesgue sampling control method was studied. First, a criterion was proposed to verify the robust set stabilization of BNs, and an algorithm was developed to design the sampled data state feedback controls (SDSFCs) within a given Lebesgue sampling region. Second, an improved sampling region was designed using the truth matrix method to reduce control update frequency while maintaining stability. Finally, the effectiveness of the proposed method was validated through a reduced model of the lac operon in Escherichia coli.

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