Detection in Adversarial Environments

Abstract

We propose new game theoretic approaches to estimate a binary random variable based on sensor measurements that may have been corrupted by a cyber-attacker. The estimation problem is formulated as a zero-sum partial information game in which a detector attempts to minimize the probability of an estimation error and an attacker attempts to maximize this probability. While this problem can be solved exactly by reducing it to the computation of the value of a matrix, this approach is computationally feasible only for a small number of sensors. The two key results of this paper provide complementary computationally efficient solutions to the construction of the optimal detector. The first result provides an explicit formula for the optimal detector but it is only valid when the number of sensors is roughly smaller than two over the probability of sensor errors. In contrast, the detector provided by the second result is valid for an arbitrary number of sensor. While it may result in a probability of estimation error that is above the minimum achievable, we show that this error is small when the number of sensors is large, which is precisely the case for which the first result does not apply.

An output‐feedback adaptive control architecture for mitigating actuator attacks in cyber‐physical systems

“…Consider the controlled dynamical system given by (11) and (12) with the corrective signal Theorem 1.…”

“…10 These attack strategies rely on perfect system knowledge availability. In the work of Vamvoudakis et al, 12 new game theoretic approaches are proposed to estimate a binary random variable based on sensor measurements that may have been corrupted by a cyber-attacker. In the work of Vamvoudakis et al, 12 new game theoretic approaches are proposed to estimate a binary random variable based on sensor measurements that may have been corrupted by a cyber-attacker.…”

“…In the work of Lucia et al, 11 a set-theoretic control framework for CPS is proposed to derive an anomaly detector module, where false data injection attacks are modeled as additive signals to sensor measurements and actuator commands. In the work of Vamvoudakis et al, 12 new game theoretic approaches are proposed to estimate a binary random variable based on sensor measurements that may have been corrupted by a cyber-attacker. An attack detection problem against deception attacks in CPS is studied in the work of Li and Chen, 13 and in the work of Li et al, 14 a security problem in CPS was studied and a remote state estimation process using multiple sensors was proposed.…”

Game Theoretical Approach to Sequential Hypothesis Test with Byzantine Sensors

“…We consider the problem of detecting a binary state using sequential analysis in the sense that stopping time is determined by observations while some other researches use a prescribed number of observed samples, e.g. one-shot scheme [19] [20] and fixed time analysis [16]. By making decision adapted to observations, Average Sample Number is saved (as can be seen in Remark 8) because sampling is stopped as soon as the existing observations possess enough preference on a certain hypothesis.…”

Autonomy and machine intelligence in complex systems: A tutorial

“…infectious diseases) [76] and social networks [10], [65], human/robot interaction systems [41], Internet [26], transportation systems [45], cyber-security (e.g. malware spreading) [2], [33], [70], [73], [82], [83], unmanned aerial/underwater vehicles [30], sensor networks [63], power networks [80] and mobile robotics [69]. Those systems are large, complex, dynamic, and highly nonlinear in their global behavior.…”