Data-Driven Safety Verification using Barrier Certificates and Matrix Zonotopes

2025-04-01

AI Summary

How to rigorously verify safety for cyber-physical systems (CPS) with model uncertainty—i.e., under unknown dynamics, measurement noise, modeling errors, and environmental disturbances? Method: We propose a model-free safety verification framework. First, we represent the uncertain system dynamics using matrix zonotopes constructed directly from noisy data, guaranteeing inclusion of the true system model. Second, we integrate this data-driven model set with barrier certificate theory to formulate a robust safety verification optimization problem. Contribution/Results: The approach requires no prior knowledge of the system dynamics and ensures mathematical rigor in safety certification while maintaining computational scalability. Numerical experiments demonstrate its efficacy in verifying safety for systems with unknown dynamics, offering both theoretical soundness and practical deployability.

Technology Category

• Reasoning under Uncertainty: Uncertainty Representations
• Multiagent Systems: Multiagent Systems under Uncertainty
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Ensuring safety in cyber-physical systems (CPSs) is a critical challenge, especially when system models are difficult to obtain or cannot be fully trusted due to uncertainty, modeling errors, or environmental disturbances. Traditional model-based approaches rely on precise system dynamics, which may not be available in real-world scenarios. To address this, we propose a data-driven safety verification framework that leverages matrix zonotopes and barrier certificates to verify system safety directly from noisy data. Instead of trusting a single unreliable model, we construct a set of models that capture all possible system dynamics that align with the observed data, ensuring that the true system model is always contained within this set. This model set is compactly represented using matrix zonotopes, enabling efficient computation and propagation of uncertainty. By integrating this representation into a barrier certificate framework, we establish rigorous safety guarantees without requiring an explicit system model. Numerical experiments demonstrate the effectiveness of our approach in verifying safety for dynamical systems with unknown models, showcasing its potential for real-world CPS applications.

Problem

• Ensuring safety in uncertain cyber-physical systems
• Verifying safety without precise system dynamics
• Using data-driven methods to handle model uncertainty

Innovation

• Data-driven safety verification using noisy data
• Matrix zonotopes for compact uncertainty representation
• Barrier certificates for model-free safety guarantees