Asymptotic Feedback Stabilization of Boolean Control Networks With Random Impulsive Disturbances
研究了受随机脉冲干扰的布尔控制网络的渐近反馈集镇定问题，将系统转化为脉冲间隔驱动的概率布尔控制网络，给出了状态反馈控制器设计算法，使系统以最少脉冲间隔收敛到目标集。
Based on the hybrid-index model, this article investigates the asymptotic feedback set stabilization of Boolean control networks (BCNs) with random impulsive disturbances. In this model, it is assumed that the sequence of intervals between adjacent impulsive instants is independent and identically distributed. This assumption ensures that the subsequence of solutions sampled at impulsive moments is a Markov chain. Based on this assumption and the semi-tensor product (STP), random impulsive BCNs (RI-BCNs) can be converted into impulsive-interval driven probabilistic BCNs (ID-PBCNs), and the input-state transition probability matrix (IS-TPM) is constructed, the calculations of convergent target set in the hybrid domain and the time domain are discussed, and the necessary and sufficient conditions for asymptotic feedback set stabilizability are obtained. On this basis, we propose a design algorithm of state feedback controllers to stabilize RI-BCNs asymptotically with respect to a target set by using state-space partition, which enables the system to converge to a given set with the least number of impulsive intervals. Finally, the effectiveness of the obtained results is verified by simulations.