Process Resilience under Optimal Data Injection Attacks

In this paper, we study the resilience of process systems in an {\it information-theoretic framework}, from the perspective of an attacker capable of optimally constructing data injection attacks. The attack aims to distract the stationary distributions of process variables and stay stealthy, simultaneously. The problem is formulated as designing a multivariate Gaussian distribution to maximize the Kullback-Leibler divergence between the stationary distributions of states and state estimates under attacks and without attacks, while minimizing that between the distributions of sensor measurements. When the attacker has limited access to sensors, sparse attacks are proposed by incorporating a sparsity constraint. {We conduct theoretical analysis on the convexity of the attack construction problem and present a greedy algorithm, which enables systematic assessment of measurement vulnerability, thereby offering insights into the inherent resilience of process systems. We numerically evaluate the performance of proposed constructions on a two-reactor process.