Local stabilization of Boolean control networks via stochastic sampled-data control

Abstract

This paper develops a stochastic sampled-data control framework for the local stabilization of Boolean control networks, where the sampling intervals are assumed to be independent and identically distributed random variables. A fundamental equivalence is established between the convergence of the full system state sequence and that of the sampled state subsequence. Based on the equivalence, we propose methods to determine the largest finite-time stabilizable region and the largest asymptotically stabilizable region, respectively. Corresponding control design strategies are provided to achieve stabilization within these regions. Moreover, a unified control scheme is proposed to simultaneously ensure both finite-time and asymptotic stabilization within their respective largest stabilizable regions. Finally, the applicability of the methods is demonstrated using two examples.