Neural Network-assisted Interval Reachability for Systems with Control Barrier Function-Based Safe Controllers
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 30 of its 50 references that are in the map. First posted on arXiv 11 Apr 2025.
Builds on
30 of 50 references.
References · 30
- 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
- 2019Control Barrier Functions: Theory and Applicationscited by 332
- 2020NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systemscited by 128
- 2019Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programmingcited by 100
- 2021Robust Control Barrier-Value Functions for Safety-Critical Controlcited by 47
- 2020Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programmingcited by 43
- 2014Reach-Avoid Problems with Time-Varying Dynamics, Targets and Constraintscited by 41
- 2021Reachability Analysis of Neural Feedback Loopscited by 41
- 2021POLAR: A Polynomial Arithmetic Framework for Verifying Neural-Network Controlled Systemscited by 38
- 2021OVERT: An Algorithm for Safety Verification of Neural Network Control Policies for Nonlinear Systemscited by 37
- 2020Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approachcited by 36
- 2019Control Barrier Functions for Systems with High Relative Degreecited by 30
18 more
- 2021Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopescited by 26
- 2022Refining Control Barrier Functions through Hamilton-Jacobi Reachabilitycited by 15
- 2023Minimum Width of Leaky-ReLU Neural Networks for Uniform Universal Approximationcited by 13
- 2023Efficient Interaction-Aware Interval Analysis of Neural Network Feedback Loopscited by 9
- 2021Safe Control Synthesis via Input Constrained Control Barrier Functionscited by 8
- 2023Interval Reachability of Nonlinear Dynamical Systems with Neural Network Controllerscited by 8
- 2022A Robust, Multiple Control Barrier Function Framework for Input Constrained Systemscited by 6
- 2023Advances in the Theory of Control Barrier Functions: Addressing Practical Challenges in Safe Control Synthesis for Autonomous and Robotic Systemscited by 6
- 2023Fast, Smooth, and Safe: Implicit Control Barrier Functions through Reach-Avoid Differential Dynamic Programmingcited by 5
- 2018On the Parameterized Computation of Minimum Volume Outer Ellipsoid of Minkowski Sum of Ellipsoidscited by 4
- 2018Reach-Avoid Problems via Sum-of-Squares Optimization and Dynamic Programmingcited by 4
- 2020Control Barrier Function based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibriacited by 3
- 2021On the Undesired Equilibria Induced by Control Barrier Function Based Quadratic Programscited by 2
- 2020Continuous Reachability Task Transition Using Control Barrier Functionscited by 1
- 2020Enforcing Safety at Runtime for Systems with Disturbancescited by 1
- 2020On Compatibility and Region of Attraction for Safe, Stabilizing Control Lawscited by 1
- 2024Characterization of the Dynamical Properties of Safety Filters for Linear Planar Systemscited by 1
- 2024Independence of Closed-Loop Equilibria and Stability from the Choice of Control Barrier Function for a Given Safe Setcited by 1
Built on by
Not cited yet.