Optimal Stabilizing Random Output Feedback for Boolean Networks With Random Data Loss

ABSTRACT This study addresses the issue of asymptotic stabilization of Boolean control networks (BCNs) through output feedback in the presence of random data loss in both output measurements and control signals. We utilize a random output feedback (ROF) strategy that employs interpolation models to compensate for missing data. A poset‐based criterion is established to determine the asymptotic stabilizability of BCNs under ROFs. Importantly, we demonstrate that data loss does not undermine asymptotic stabilizability, provided that the probability of data loss is strictly less than one. Furthermore, we explore the problem of designing an optimal stabilizing ROF. An algorithm is presented to compute the optimal stabilizing ROF based on linear matrix inequalities (LMIs) with equality constraints. The proposed method is applied to control a simplified BCN model for the lac operon in the bacterium Escherichia coli . The results reveal that the optimal ROF strategy outperforms the optimal deterministic output feedback (DOF) strategy.