Topological Structure, Reachability, and Stabilization of Constrained Boolean Control Networks via Event-Triggered Control

This paper is concerned with the topological structure, reachability, and stabilization for Boolean control networks (BCNs) with state constraints via event-triggered control (ETC) scheme. In the first part, the topological structure of BCNs with state constraints is studied. Under the framework of state constrain, the definitions of fixed point and cycle are first defined. A novel phenomenon is that there may exist two kinds constrained fixed points, which are, respectively, named as the livelock and deadlock ones. It is different with the traditional fixed point. Accordingly, a formula is presented to calculate the number of constrained fixed points and constrained cycles. In the second part, the constrained reachability and stabilization problem of the event-triggered controlled BCNs are investigated. Two necessary and sufficient criteria are, respectively, obtained. Furthermore, an algorithm is developed to design all feasible controllers. Finally, a reduced model of the lac operon in the Escherichia coli is shown to illustrate the efficiency of the obtained results.