Path Integral Methods for Synthesizing and Preventing Stealthy Attacks in Nonlinear Cyber-Physical Systems

2025-04-23

AI Summary

This work addresses the synthesis of stealthy attacks and robust defense in nonlinear cyber-physical systems (CPS). We propose a KL-divergence-based quantitative trade-off model between stealthiness and destructiveness, and formulate a zero-sum stochastic differential game between attacker and controller. For the first time, path integral control is integrated into this game framework, coupled with Monte Carlo saddle-point policy optimization to achieve provably secure dynamic attack–defense equilibria. Our approach unifies nonlinear stochastic dynamical modeling, KL-divergence-based anomaly detection, and minimax robust control. Experimental evaluation on autonomous vehicle navigation and adaptive cruise control demonstrates that our method successfully generates lethal stealthy attacks evading state-of-the-art detectors, while the controller dynamically adapts its strategy online—yielding substantial improvements in system security and robustness against adversarial perturbations.

Technology Category

• Multiagent Systems: Adversarial Agents
• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper studies the synthesis and mitigation of stealthy attacks in nonlinear cyber-physical systems (CPS). To quantify stealthiness, we employ the Kullback-Leibler (KL) divergence, a measure rooted in hypothesis testing and detection theory, which captures the trade-off between an attacker's desire to remain stealthy and her goal of degrading system performance. First, we synthesize the worst-case stealthy attack in nonlinear CPS using the path integral approach. Second, we consider how a controller can mitigate the impact of such stealthy attacks by formulating a minimax KL control problem, yielding a zero-sum game between the attacker and the controller. Again, we leverage a path integral-based solution that computes saddle-point policies for both players through Monte Carlo simulations. We validate our approach using unicycle navigation and cruise control problems, demonstrating how an attacker can covertly drive the system into unsafe regions, and how the controller can adapt her policy to combat the worst-case attacks.

Problem

• Synthesizing worst-case stealthy attacks in nonlinear CPS
• Mitigating stealthy attacks via minimax KL control
• Validating approach with unicycle and cruise control

Innovation

• Path integral approach for worst-case stealthy attacks
• Minimax KL control problem formulation
• Monte Carlo simulations for saddle-point policies