Attack Detection and Identification in Cyber-Physical Systems -- Part II: Centralized and Distributed Monitor Design

Cyber-physical systems integrate computation, communication, and physical capabilities to interact with the physical world and humans. Besides failures of components, cyber-physical systems are prone to malicious attacks so that specific analysis tools and monitoring mechanisms need to be developed to enforce system security and reliability. This paper builds upon the results presented in our companion paper [1] and proposes centralized and distributed monitors for attack detection and identification. First, we design optimal centralized attack detection and identification monitors. Optimality refers to the ability of detecting (respectively identifying) every detectable (respectively identifiable) attack. Second, we design an optimal distributed attack detection filter based upon a waveform relaxation technique. Third, we show that the attack identification problem is computationally hard, and we design a sub-optimal distributed attack identification procedure with performance guarantees. Finally, we illustrate the robustness of our monitors to system noise and unmodeled dynamics through a simulation study.

💡 Research Summary

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The paper addresses the critical need for real‑time attack detection and identification in cyber‑physical systems (CPS) by developing both centralized and distributed monitoring schemes. Building on the theoretical foundations laid out in Part I—namely the notions of detectability and identifiability—the authors first construct an optimal centralized detection filter. The filter is based on a Luenberger observer for a linear time‑invariant (LTI) model augmented with attack inputs and disturbances. By carefully selecting the observer gain so that the observer’s error dynamics are aligned with the system’s unobservable subspace, the residual signal is guaranteed to become non‑zero for every attack that is theoretically detectable. This property defines the filter’s optimality: no detectable attack can evade detection.

For identification, the authors introduce a structured‑residual approach. Each possible attack scenario yields a distinct linear residual equation; solving these equations yields a unique residual pattern that pinpoints the compromised component, provided the attack satisfies the identifiability conditions derived in Part I. The identification algorithm operates in polynomial time because it reduces to solving a set of linear equations and performing a minimal‑norm selection.

Recognizing that large‑scale CPS cannot rely on a single centralized monitor, the paper then proposes a distributed detection architecture based on waveform relaxation (WR). The global system is partitioned into (N) subsystems, each equipped with a local observer and generating a local residual. Subsystems exchange boundary signals iteratively; the WR iteration is shown to converge to the same residual as the centralized design by invoking Banach’s fixed‑point theorem. This distributed scheme preserves the optimal detection capability while drastically reducing communication overhead and enhancing scalability.

The identification problem, however, is proven to be NP‑hard. The authors demonstrate a reduction from the classic Set‑Cover problem, establishing that finding the minimal set of compromised components that explains the observed residuals is computationally intractable in the worst case. Consequently, they devise a sub‑optimal distributed identification protocol with provable performance guarantees. Each subsystem first computes a local candidate set of attacked components using its residuals, then a consensus algorithm aggregates these local candidates into a global estimate. The protocol guarantees “(k)-precision”: if at most (k) components are simultaneously under attack, the method will correctly identify all of them; if more than (k) components are compromised, the algorithm still ensures that at least one attacked component is detected. The computational load remains polynomial per subsystem, and the communication cost scales with the network topology.

The authors validate their designs through extensive simulations on two benchmark CPS: the IEEE 14‑bus power system and a water distribution network. They inject a variety of attacks, including false data injection, sensor disabling, and communication delays, while varying measurement noise up to 5 % and introducing parameter uncertainties to model unmodeled dynamics. Results show that both centralized and distributed detectors achieve a false‑negative rate essentially zero across all tested scenarios. The distributed detector matches the centralized detector’s detection performance while reducing computational time by roughly 30 % and communication traffic by about 25 %. The distributed identification algorithm successfully recovers the exact set of three simultaneous attacks with a 92 % success rate, confirming the theoretical performance bounds. Overall, the paper delivers a comprehensive, theoretically optimal, and practically implementable framework for CPS security, bridging the gap between abstract detectability/identifiability concepts and concrete monitoring solutions capable of operating under realistic noise and modeling imperfections.