This paper investigates equilibrium strategies in networked control systems subject to false data injection (FDI) attacks, employing a game-theoretic approach. Our framework characterizes the dynamics that revolves around the freshness of the data from multiple sensors using the age of incorrect information (AoII) metric. The interaction between legitimate transmitters, aiming to minimize the system AoII and their transmission costs, and a malicious adversary, aiming to maximize AoII while managing FDI costs, is modeled as a non-cooperative game. We analytically demonstrate the existence and uniqueness of a Nash equilibrium (NE) and derive explicit conditions characterizing equilibrium resource allocation strategies. We also present examples of applications related to secure healthcare and automotive control. The numerical results validate our theoretical findings, highlighting the strategic impact of the system parameters, including drift rates, FDI and transmission costs, and resource constraints. Our analysis yields actionable guidelines for enhancing sensor security through parameter tuning and resource allocation.

We study a control system where sensor measurements are transmitted to a remote station. Information may become outdated due to system drift or compromised by malicious false data injection. To quantify the impact of staleness and inaccuracy in the information at the receiver’s side, we use Age of Incorrect Information (AoII). In particular, we consider the Excess AoII above a certain threshold as our key objective to minimize, which we argue to be a sensible goal for many real-time control systems. We adopt a game-theoretic framework to model the strategic interaction between a transmitter, which aims to minimize both Excess AoII and transmission costs, and a malicious agent, which seeks to maximize the same Excess AoII metric while minimizing its own costs. Our analysis reveals the existence of a Nash equilibrium for this game, and we investigate how the system parameters influence the adversary’s decision to attack, identifying the conditions under which an attack becomes advantageous or not.

We use Bayesian game theory to investigate the interaction between a system controller and an additional unknown agent in a cyber-physical system. The system controller performs some monitoring for real-time operation management, with the aim of minimizing the age of incorrect information (AoII). The additional agent reports some extra information, which ideally can serve to aid the controller and meet the same objective of decreasing AoII, but it is uncertain whether these actions are useful or correspond to (possibly international) false data injection in the system. The controller only has information in terms of probability of the legitimacy of this extra agent through a common prior, and also knows that, in case it is malicious, it will try to increase AoII instead. Our analysis reveals that, under rational behavior, an adversary can effectively masquerading as a sensor injecting legitimate data, as the controller can hardly distinguish the behavior of a true helper from that of an attacker. However, under variable data drift, the strategic behavior of the external agent can give away their type.

In the era of Industry 5.0, securing Industrial Control Systems (ICS) is increasingly vital, especially when relying on legacy communication protocols like Modbus TCP that may lack built-in protection mechanisms. This paper addresses the challenge of preserving the confidentiality of internal system states from potential cyber adversaries through a security-by-design framework. We propose a novel approach that leverages Discrete Event Systems (DES) theory to model communication flows and applies probabilistic opacity to quantify the risk of state disclosure. Central to our method is the concept of selective encryption: instead of encrypting all messages, we strategically encrypt only those events that could reveal sensitive information. This gives rise to a budget-constrained optimization problem, where the goal is to enforce opacity under resource limitations. To solve this efficiently, we develop a greedy algorithm that maximizes security by allocating encryption effort to the most critical events. The proposed method is validated using a representative example featuring two distinct query types, demonstrating its capability to limit information leakage while keeping low the computational overhead.