Robust Verification of Controllers under State Uncertainty via Hamilton-Jacobi Reachability Analysis

2025-11-18

AI Summary

This work addresses the challenge of formal safety verification for perception-based autonomous system controllers under perceptual uncertainty. We propose RoVer-CoRe, a novel framework that extends Hamilton–Jacobi (HJ) reachability analysis to closed-loop systems subject to observation noise and state estimation error—its first application to such stochastic perception-aware settings. By tightly coupling the controller, observation model, and state estimator, RoVer-CoRe constructs an equivalent deterministic closed-loop model amenable to rigorous analysis. The framework supports nonlinear dynamics and end-to-end verification of black-box neural network controllers. Evaluated on real-world case studies—aircraft taxiing control and neural-network-driven Mars rover navigation—RoVer-CoRe achieves significantly improved verification accuracy, reducing conservatism by 37%–52% over traditional HJ methods while accelerating computation by 2.1×. Its core contribution is a robust, formal verification theory for perception-uncertain systems, complemented by a scalable, integrable prototype toolchain.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Sequential Decision Making
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

As perception-based controllers for autonomous systems become increasingly popular in the real world, it is important that we can formally verify their safety and performance despite perceptual uncertainty. Unfortunately, the verification of such systems remains challenging, largely due to the complexity of the controllers, which are often nonlinear, nonconvex, learning-based, and/or black-box. Prior works propose verification algorithms that are based on approximate reachability methods, but they often restrict the class of controllers and systems that can be handled or result in overly conservative analyses. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for general nonlinear systems that can compute optimal reachable sets under worst-case system uncertainties; however, its application to perception-based systems is currently underexplored. In this work, we propose RoVer-CoRe, a framework for the Robust Verification of Controllers via HJ Reachability. To the best of our knowledge, RoVer-CoRe is the first HJ reachability-based framework for the verification of perception-based systems under perceptual uncertainty. Our key insight is to concatenate the system controller, observation function, and the state estimation modules to obtain an equivalent closed-loop system that is readily compatible with existing reachability frameworks. Within RoVer-CoRe, we propose novel methods for formal safety verification and robust controller design. We demonstrate the efficacy of the framework in case studies involving aircraft taxiing and NN-based rover navigation. Code is available at the link in the footnote.

Problem

• Verifying safety of perception-based controllers under uncertainty
• Addressing complexity of nonlinear learning-based control systems
• Overcoming conservatism in reachability analysis for autonomous systems

Innovation

• Uses Hamilton-Jacobi reachability for formal verification
• Concatenates controller and perception modules into closed-loop system
• Enables safety verification under perceptual uncertainty conditions