Set Stabilization of Probabilistic Boolean Control Networks: A Sampled-Data Control Approach.

Abstract

This article investigates the set stabilization of probabilistic Boolean control networks (PBCNs) under sampled-data (SD) state-feedback control within finite and infinite time, respectively. First, the algorithms are, respectively, proposed to find the sampled point set and the largest sampled point control invariant set (SPCIS) of PBCNs by SD state-feedback control. Based on this, a necessary and sufficient criterion is proposed for the global set stabilization of PBCNs by SD state-feedback control within finite time. Moreover, the time-optimal SD state-feedback controller is designed. It is interesting that if the sampled period (SP) is changed, the time of global set stabilization of PBCNs may also change or even the PBCNs cannot achieve set stabilization. Second, a criterion for the global set stabilization of PBCNs by SD state-feedback control within infinite time is obtained. Furthermore, all possible SD state-feedback controllers are obtained by using all the complete families of reachable sets. Finally, three examples are presented to illustrate the effectiveness of the obtained results.