Set stabilization of Boolean control networks with disturbance inputs via self-triggered control

The research on robust control of Boolean networks provides core technical support for the stable and reliable operation of complex discrete systems such as gene regulatory networks and power systems under disturbances. In previous studies, several kinds of controllers have been proposed to achieve the robust set stabilization of Boolean control networks with disturbance inputs (DBCNs). However, a key issue with the currently methods is that the controls usually update more frequently than necessary. To address this issue, this paper investigates the problem of self-triggered controller design for robust set stabilization of DBCNs. First, the definition of Lyapunov function (LF) for set stabilization of DBCNs is proposed, and an algorithm to construct the LF using truth-matrix technique is designed. Then, a necessary and sufficient condition for the set stabilization of DBCNs under the LF method is presented. Based on the obtained LF, a kind of self-triggered controllers is designed such that the system can robustly stabilize to a desired state set. Compared with existing control schemes for robust set stabilization of DBCNs, the self-triggered controllers we designed can effectively reduce the control update frequency, thereby lowering the control cost. Finally, two examples are provided to validate the efficiency of the obtained results.