Robust Output Tracking of Boolean Control Networks Subject to Stochastic Function Perturbations

This article explores the influence of stochastic function perturbations (SFPs) on the output tracking of Boolean control networks (BCNs). First, by establishing the transition probability matrix of BCNs subject to SFPs, a criterion is presented to verify whether or not the state transition of BCNs is affected by SFPs. Second, when the state transition of BCNs is influenced by SFPs, a perturbed parameterized set is constructed via the information of original BCNs and SFPs. Based on the perturbed parameterized set, several necessary and sufficient conditions are derived for the robust output tracking of BCNs subject to SFPs, including keeping finite-time output tracking and reducing to asymptotic output tracking. Finally, the obtained theoretical results are applied to a Boolean model of lac operon in the Escherichia coli.