Delay Independent Safe Control with Neural Networks: Positive Lur'e Certificates for Risk Aware Autonomy

2025-10-08

AI Summary

This paper addresses the safety certification problem for neural network controllers under state/input delays and interval matrix uncertainties. We propose a risk-aware control method based on positive Lur’e systems. Our key contribution is the first use of a positive Lur’e structure to construct linear, delay-independent safety certificates—bypassing traditional integral quadratic constraint (IQC) frameworks that require explicit delay modeling and suffer from semidefinite programming (SDP) scalability bottlenecks. By characterizing neural network nonlinearities via local sector bounds and integrating positivity analysis with IQC verification, we achieve efficient certification of local exponential stability. Experiments demonstrate that our approach accelerates verification by several orders of magnitude compared to SDP-based IQC methods, while successfully certifying safety over significantly larger uncertainty intervals previously infeasible—thereby substantially expanding the scope of scalable, formal safety guarantees.

Technology Category

• Natural Language Processing: Safety and Robustness
• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

We present a risk-aware safety certification method for autonomous, learning enabled control systems. Focusing on two realistic risks, state/input delays and interval matrix uncertainty, we model the neural network (NN) controller with local sector bounds and exploit positivity structure to derive linear, delay-independent certificates that guarantee local exponential stability across admissible uncertainties. To benchmark performance, we adopt and implement a state-of-the-art IQC NN verification pipeline. On representative cases, our positivity-based tests run orders of magnitude faster than SDP-based IQC while certifying regimes the latter cannot-providing scalable safety guarantees that complement risk-aware control.

Problem

• Addresses safety certification for autonomous systems with delays
• Handles neural network controllers under input delays and uncertainties
• Provides scalable stability guarantees faster than existing methods

Innovation

• Delay-independent certificates for neural network control
• Positive Lur'e structure ensures exponential stability
• Faster verification than SDP-based IQC methods