Reachability Analysis of Cyber-Physical Systems Under Stealthy Attacks

Area of Science:

• Control Systems Engineering
• Cybersecurity
• Estimation Theory

Background:

• Cyber-physical systems (CPS) are vulnerable to stealthy attacks that evade detection.
• Kalman filters are crucial for state estimation in CPS but can be compromised by sophisticated attacks.
• Quantifying the impact of stealthy attacks on system state and estimation error is essential for robust system design.

Purpose of the Study:

• To define and analyze the reachable set of CPS under stealthy attacks.
• To establish conditions for the boundedness of the reachable set.
• To develop an ellipsoidal approximation for safety evaluation and demonstrate its application.

Main Methods:

• Utilizing Kullback-Leibler divergence to quantify attack stealthiness.
• Defining the reachable set incorporating system state and Kalman filter estimation error.
• Deriving necessary and sufficient conditions for unbounded reachable sets (finite and infinite time).
• Employing convex optimization to obtain an ellipsoidal outer approximation for bounded reachable sets.

Main Results:

• Characterization of conditions under which the reachable set becomes unbounded.
• Development of a computationally tractable ellipsoidal outer approximation for bounded reachable sets.
• Demonstration of the approximation's utility in safety evaluation.
• Validation of the proposed methodology through a numerical simulation on an unmanned ground vehicle.

Conclusions:

• The study provides a rigorous framework for analyzing the impact of stealthy attacks on CPS.
• The derived ellipsoidal approximation offers a practical tool for assessing system safety under adversarial conditions.
• The findings are crucial for designing resilient and secure cyber-physical systems.