Stabilizing Logical Networks with Stochastic State-Heritable Control: A Markovian Sampling Method

This paper investigates asymptotic stabilization for heritable logical control networks (HLCNs). A pioneering method is proposed to deal with heritable hidden information, a stochastic temporal sequence that unavoidably exists in many practical controllers. To capture such information, a gated recurrent unit structure is introduced, in which the gate mechanism is modeled by a Markovian sampling process. Based on that, the semitensor product is applied to formulate the system as a switched LCN with a time-varying dimension. Then, the matrix expansion technique is employed to unify the dimension, and necessary and sufficient criteria for asymptotic stabilization are derived in two typical cases of the heritable hidden information. All of these criteria can be implemented using a newly proposed algorithm that is applicable to general cases. Finally, two illustrative examples are presented to validate the theoretical results.