Modular Verification of Opacity for Interconnected Control Systems via Barrier Certificates

Abstract

In this letter, we consider the problem of verifying initial-state opacity for networks of discrete-time control systems. We formulate the opacity property as a safety one over an appropriately constructed augmented system, and aim to verify this latter property by finding suitable barrier certificates. To reduce the computational complexity associated with computing barrier certificates for large networks, we propose a compositional approach to construct such barrier certificates for large-scale interconnected systems. This is achieved by introducing local barrier certificates for subsystems in the network and imposing some small-gain type conditions on the gains of those local barrier certificates. We also provide sufficient conditions for verifying the lack of opacity in large-scale networks by constructing barrier certificates ensuring some reachability properties over the augmented systems. To illustrate the effectiveness of our results, we consider the problem of tracking a target using a team of vehicles and verify if its initial position is secret from possible outside intruders.