Event-Triggered Robust Synchronization of Probabilistic Boolean Networks: Robust Invariant Set Approach

In this article, we consider event-triggered control (ETC) to achieve robust synchronization between Boolean networks and probabilistic Boolean networks (PBNs). The advantage of the controller in this article lies in its robustness against random disturbances, which unavoidably exist in real networks because of environmental changes. Moreover, the proposed ETC effectively reduces energy consumption, because it achieves the control objective using the shortest possible time without unnecessary updates of the feedback gain. First, robust synchronization is equivalently converted to robust set stabilization of an augmented PBN using the semitensor product. Second, a feasible algorithm is presented to calculate the largest robust control invariant set of a given set, based on which a necessary and sufficient condition is developed for the existence of event-triggered controllers. Then, a detailed configuration of all feasible controllers is provided by a constructive algorithm. Under some mild conditions, global controllers are designed to further reduce computation load. Finally, examples are provided to illustrate the main results.