[Paper Review] Networked Control under Random and Malicious Packet Losses

Ahmet Cetinkaya, Hideaki Ishii+1 more|arXiv (Cornell University)|Jun 16, 2016

Smart Grid Security and Resilience50 references3 citations

TL;DR

This paper proposes a unified probabilistic model for analyzing combined random and malicious packet losses in networked control systems. By characterizing failure rates via tail probability conditions and using event-triggered control with Lyapunov-like functions, it establishes sufficient conditions for almost sure asymptotic stabilization and identifies attack strategies that induce instability, with numerical validation showing critical thresholds for instability under selective attacks.

ABSTRACT

We study cyber security issues in networked control of a linear dynamical system. Specifically, the dynamical system and the controller are assumed to be connected through a communication channel that face malicious attacks as well as random packet losses due to unreliability of transmissions. We provide a probabilistic characterization for the link failures which allows us to study combined effects of malicious and random packet losses. We first investigate almost sure stabilization under an event-triggered control law, where we utilize Lyapunov-like functions to characterize the triggering times at which the plant and the controller attempt to exchange state and control data over the network. We then provide a look at the networked control problem from the attacker's perspective and explore malicious attacks that cause instability. Finally, we demonstrate the efficacy of our results with numerical examples.

Motivation & Objective

• To address the growing cyber security threat in industrial control systems due to unreliable communication channels prone to both random failures and malicious attacks.
• To develop a general probabilistic framework that unifies the analysis of random packet losses and malicious attacks in networked control systems.
• To investigate the stability of event-triggered control under combined random and malicious packet losses, including worst-case attack scenarios.
• To provide sufficient conditions for almost sure asymptotic stabilization under the proposed model, with explicit design guidelines for feedback gains.
• To analyze the attacker's perspective and identify conditions under which malicious attacks can destabilize the system despite random losses.

Proposed method

• Introduces a tail probability condition on the average number of packet exchange failures to unify random and malicious loss models.
• Models random losses using a time-inhomogeneous binary-valued Markov chain to capture time-varying reliability.
• Uses a malicious attack model inspired by reactive jamming, where attacks are bounded almost surely and can depend on random loss states.
• Applies Lyapunov-like functions to characterize event-triggering instants and derive stability conditions for the closed-loop system.
• Employs a feedback gain redesign strategy to restore stability when attacks exceed safe thresholds.
• Validates results through numerical simulations under various attack strategies, including state-dependent and selective attacks.

Experimental results

Research questions

• RQ1 How can random and malicious packet losses be modeled in a unified probabilistic framework for networked control systems?
• RQ2 Under what conditions is almost sure asymptotic stabilization achievable in the presence of both random and malicious packet losses?
• RQ3 What attack strategies can destabilize a networked control system, and how do they interact with random transmission failures?
• RQ4 How does the dependence between attack strategies and random loss events affect system stability?
• RQ5 Can feedback gains be redesigned to restore stability when malicious attacks exceed safe thresholds?

Key findings

• The proposed model captures both random losses and malicious attacks—such as reactive jamming—within a single probabilistic framework using tail probability conditions.
• For independent random and malicious losses, the system remains almost surely asymptotically stable if the combined failure rate is below a threshold derived from the Lyapunov function analysis.
• With a selective attack strategy (72) that avoids attacking during random loss events, the system diverges when the average failure rate exceeds σ = 0.7, satisfying the instability condition (57) in Theorem IV.2.
• Numerical results show that under attack (72) with τ = 3, the average number of failures approaches 2/3, which acts as a critical threshold: ρ < 2/3 implies stability, σ > 2/3 implies instability.
• When attacks depend on system state (e.g., only when ln V(x(t)) ≤ ζ), the attacker can maintain the system near a bounded level (ζ = 50), demonstrating persistent destabilization without full divergence.
• Redesigning the feedback gain to K = -1.9 ensures almost sure asymptotic stability even under the same attack strategy, as the combined failure rate ρ = 0.744 remains below the stability threshold.