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

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.