Verification of approximate opacity for switched systems: A compositional approach

The security in information-flow has become a major concern for cyber–physical systems (CPSs). In this work, we focus on the analysis of an information-flow security property, called opacity. Opacity characterizes the plausible deniability of a system’s secret in the presence of a malicious outside intruder. We propose a methodology of checking a notion of opacity, called approximate opacity, for networks of discrete-time switched systems. Our framework relies on compositional constructions of finite abstractions for networks of switched systems and their approximate opacity-preserving simulation functions. Those functions characterize how close concrete networks and their finite abstractions are in terms of the satisfaction of approximate opacity. We show that such simulation functions can be obtained compositionally by assuming some small-gain type conditions and composing local simulation functions constructed for each switched subsystem separately. Additionally, assuming certain stability property of switched systems, we also provide a technique on constructing their finite abstractions together with the corresponding local simulation functions. Finally, we illustrate the effectiveness of our results through an example.