Algebraic analysis and control of networked opacity with bounded communication delays

Networked finite state machine takes the delay factor into consideration, and its security has become an significant research topic. In this paper, we explore the impact of bounded communication delays on networked opacity of finite state machine from an algebraic point. Firstly, by making use of Boolean semi-tensor product (Boolean STP), we propose an algebraic equation to characterize the current dynamics with bounded observation delays. Subsequently, we give the verification criterion for networked opacity, and calculate the delayed dynamics by introducing the state reachability matrix. Meanwhile, we investigate the effect of bound number on the opacity-enforcement problem, and compute the minimum bound of communication delay to ensure the state opacity property. Finally, a numerical example is provided to demonstrate the results.