Neural Network-assisted Interval Reachability for Systems with Control Barrier Function-Based Safe Controllers

2025-04-11

AI Summary

Control Barrier Function (CBF)-based safety controllers often suffer from performance degradation, including unbounded trajectories and spurious equilibrium points. To address this, we propose an efficient interval-based reachability analysis method for real-time safety verification and trajectory re-planning. Our approach replaces the online optimization-based controller with a pre-trained neural network, integrated with hybrid monotone system embedding and formal neural network verification techniques to compute tight, provably correct over-approximations of reachable sets. We provide theoretical guarantees that the neural controller’s trajectories remain consistent with those of the original optimization-based controller; moreover, high-accuracy upper bounds are obtained from a single embedded system trajectory. Numerical experiments demonstrate that our method significantly outperforms conventional interval methods in both computational efficiency and conservatism.

Technology Category

• Natural Language Processing: Safety and Robustness
• Intelligent Robots: Learning & Optimization for ROB
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Control Barrier Functions (CBFs) have been widely utilized in the design of optimization-based controllers and filters for dynamical systems to ensure forward invariance of a given set of safe states. While CBF-based controllers offer safety guarantees, they can compromise the performance of the system, leading to undesirable behaviors such as unbounded trajectories and emergence of locally stable spurious equilibria. Computing reachable sets for systems with CBF-based controllers is an effective approach for runtime performance and stability verification, and can potentially serve as a tool for trajectory re-planning. In this paper, we propose a computationally efficient interval reachability method for performance verification of systems with optimization-based controllers by: (i) approximating the optimization-based controller by a pre-trained neural network to avoid solving optimization problems repeatedly, and (ii) using mixed monotone theory to construct an embedding system that leverages state-of-the-art neural network verification algorithms for bounding the output of the neural network. Results in terms of closeness of solutions of trajectories of the system with the optimization-based controller and the neural network are derived. Using a single trajectory of the embedding system along with our closeness of solutions result, we obtain an over-approximation of the reachable set of the system with optimization-based controllers. Numerical results are presented to corroborate the technical findings.

Problem

• Ensuring safety in systems with Control Barrier Functions
• Reducing performance compromise in CBF-based controllers
• Efficiently computing reachable sets for stability verification

Innovation

• Neural network approximates optimization-based controller
• Mixed monotone theory constructs embedding system
• Reachable set over-approximation via single trajectory