Sampled-Data State Feedback Control for the Set Stabilization of Boolean Control Networks

Abstract

This paper studies the set stabilization of Boolean control networks (BCNs) under sampled-data state feedback control (SDSFC). The main research content is divided into two parts. First, the topological structure of BCNs under given SDSFC is investigated. The fixed point and sampled cycle are defined, respectively. It is found that sampled cycles allow elements to be repeated and not every element can be regarded as an initial state, and this is quite different from conventional cycles of BCNs. A theorem is presented to calculate the number of fixed points and an algorithm is given to find all fixed points and sampled cycles. Second, the set stabilization problem of BCNs by SDSFC is investigated based on the sampled point set and the sampled point control invariant set (SPCIS). A necessary and sufficient condition is derived for the global set stabilization of BCNs by SDSFC, and further sampled-data state feedback controllers are also designed. The interesting thing is that if a state enters the SPCIS as an unsampled point, then it may run out of the given set again, which is in sharp contrast to conventional BCNs. Finally, an example is given to illustrate the efficiency of the obtained results.