Asynchronous event-based set stabilization of logical control networks and its applications in finite-field networks

In this paper, the asynchronous event-triggered control mechanism (AETCM) is introduced to the set stabilization problem of k-valued logical control networks (KVLCNs). Under the proposed AETCM, each node of the system updates its event-triggered instants independently. In this case, how to coordinate the behaviors of various nodes is a challenge for us. As to this paper, we firstly transform the set stabilization problem of KVLCNs into the shortest path problem in graph theory and then construct a weighted directed hypergraph. Next, an improved heap-optimized Dijkstra algorithm is designed for the optimal asynchronous event-triggered controller. Furthermore, we study set stabilization of KVLCNs with time delays. In terms of applications, how to flexibly adapt AETCM to specific models is a difficult problem. In this paper, as applications, consensus of finite-field networks (FFNs) with arbitrary communication delays and synchronization of KVLCNs are investigated. Finally, two numerical examples are shown to illustrate the effectiveness of the proposed algorithms.