Biblio

Our position is that a key component of securing cyber-physical systems (CPS) is to develop a theory of accountability that encompasses both control and computing systems. We envision that a unified theory of accountability in CPS can be built on a foundation of causal information flow analysis. This theory will support design and analysis of mechanisms at various stages of the accountability regime: attack detection, responsibility-assignment (e.g., attack identification or localization), and corrective measures (e.g., via resilient control) As an initial step in this direction, we summarize our results on attack detection in control systems. We use the Kullback-Liebler (KL) divergence as a causal information flow measure. We then recover, using information flow analyses, a set of existing results in the literature that were previously proved using different techniques. These results cover passive detection, stealthy attack characterization, and active detection. This research direction is related to recent work on accountability in computational systems [1], [2], [3], [4]. We envision that by casting accountability theories in computing and control systems in terms of causal information flow, we can provide a common foundation to develop a theory for CPS that compose elements from both domains.

In this paper a novel set-theoretic control framework for Cyber-Physical Systems is presented. By resorting to set-theoretic ideas, an anomaly detector module and a control remediation strategy are formally derived with the aim to contrast cyber False Data Injection (FDI) attacks affecting the communication channels. The resulting scheme ensures Uniformly Ultimate Boundedness and constraints fulfillment regardless of any admissible attack scenario.

A distributed cyber control system comprises various types of assets, including sensors, intrusion detection systems, scanners, controllers, and actuators. The modeling and analysis of these components usually require multi-disciplinary approaches. This paper presents a modeling and dynamic analysis of a distributed cyber control system for situational awareness by taking advantage of control theory and time Petri net. Linear time-invariant systems are used to model the target system, attacks, assets influences, and an anomaly-based intrusion detection system. Time Petri nets are used to model the impact and timing relationships of attacks, vulnerability, and recovery at every node. To characterize those distributed control systems that are perfectly attackable, algebraic and topological attackability conditions are derived. Numerical evaluation is performed to determine the impact of attacks on distributed control system.

We consider the estimation of a scalar state based on m measurements that can be potentially manipulated by an adversary. The attacker is assumed to have full knowledge about the true value of the state to be estimated and about the value of all the measurements. However, the attacker has limited resources and can only manipulate up to l of the m measurements. The problem is formulated as a minimax optimization, where one seeks to construct an optimal estimator that minimizes the “worst-case” expected cost against all possible manipulations by the attacker. We show that if the attacker can manipulate at least half the measurements (l ≥ m/2), then the optimal worst-case estimator should ignore all measurements and be based solely on the a-priori information. We provide the explicit form of the optimal estimator when the attacker can manipulate less than half the measurements (l <; m/2), which is based on (m2l) local estimators. We further prove that such an estimator can be reduced into simpler forms for two special cases, i.e., either the estimator is symmetric and monotone or m = 2l + 1. Finally we apply the proposed methodology in the case of Gaussian measurements.

A distributed cyber control system comprises various types of assets, including sensors, intrusion detection systems, scanners, controllers, and actuators. The modeling and analysis of these components usually require multi-disciplinary approaches. This paper presents a modeling and dynamic analysis of a distributed cyber control system for situational awareness by taking advantage of control theory and time Petri net. Linear time-invariant systems are used to model the target system, attacks, assets influences, and an anomaly-based intrusion detection system. Time Petri nets are used to model the impact and timing relationships of attacks, vulnerability, and recovery at every node. To characterize those distributed control systems that are perfectly attackable, algebraic and topological attackability conditions are derived. Numerical evaluation is performed to determine the impact of attacks on distributed control system.