Design of Stealthy Joint Attacks Against Cyber-Physical Systems: A Reachable Set Approach

This article studies the joint design of stealthy actuator and sensor attacks against cyber-physical systems with the aim of keeping the system’s state in an unsafe region. The Kullback-Leibler divergence is adopted as the metric of the joint attacks’ stealthiness. The attacker’s objective is realized by making the system’s ellipsoidal invariant reachable set under stealthy joint attacks belong to the unsafe set. Firstly, the relationship between the actuator attack and the shape of the ellipsoid is analyzed and it can be characterized by a non-convex optimization problem. Parameters of the actuator attack are obtained by solving another convex optimization problem constructed through applying a linear transformation to the original problem. Then, the sensor attack is analytically solved from a non-convex optimization problem to move the center of the ellipsoid to the desired target and increase the controller’s cost. Finally, an example of the flotation industrial process is illustrated to demonstrate effectiveness of the attack.