A Probabilistic Approach to Design Switching Attacks against Interconnected Systems

In this paper we study an attack design problem for interconnected systems where the attacker compromises a subsystem at each time, which is selected randomly based on a pre-computed probabilistic rule. The objective of the attacker is to degrade the system performance, which is measured based on a quadratic function of the system state, while remaining undetected from a centralized detector. First, we derive an explicit expression for the detection probability, analyze its properties, and compute an upper bound. Then, we use our upper bound to formulate and numerically solve a non-convex optimization problem for the computation of optimal attack strategies. Finally, we validate our results and show that our probabilistic attack strategy outperforms a deterministic attack strategy that compromises a fixed subsystem at each time.