Networked opacity for finite state machine with bounded communication delays

Abstract

Networked finite state machines consider the delay factor in real-time communication networks, and the security has become an important research topic in cyber-physical systems (CPSs). In this brief paper, we explore the networked opacity of finite state machine with bounded communication delays. Firstly, the networked opacity is proposed from the perspective of security state reachability, and by use of the Boolean matrix semi-tensor product (STP), we introduce the reachability matrix with respect to all feasible events to give the current dynamics with bounded communication delays. Subsequently, based on the algebraic equation, we continue to discuss the corresponding current estimate of possible reachable states, which can be calculated by a matrix approach. Then, a more simple and effective verification criterion of networked opacity is derived by some matrix manipulations. Finally, a typical example is provided to validate the impact of communication delay on the opacity of CPSs, and our results contribute to deeply understanding the information security in the area of CPSs.