Asynchronous Event-Based Set Stabilization of Logical Control Networks and its Applications in Finite-Field Networks

Abstract

In this article, the asynchronous event-triggered control mechanism (AETCM) is introduced to the set stabilization problem of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -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 for this article, we first 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 the AETCM to specific models is a difficult problem. In this article, as applications, the consensus of finite-field networks with arbitrary communication delays and synchronization of KVLCNs is investigated. Finally, two numerical examples are shown to illustrate the effectiveness of the proposed algorithms.