2023/12/13 by Han Wang, Wang, Han, Zuxun Xiong +5 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Adversarial Robustness in Machine Learning #FOS: Mathematics #Fault Detection and Control Systems #Model Reduction and Neural Networks #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2312.08293
openalex publication_date 2023/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Neural network controllers have shown potential in achieving superior performance in feedback control systems. Although a neural network can be trained efficiently using deep and reinforcement learning methods, providing formal guarantees for the closed-loop properties is challenging. The main difficulty comes from the nonlinear activation functions. One popular method is to use sector bounds on the activation functions resulting in a robust analysis. These methods work well under the assumption that the system dynamics are perfectly known, which is, however, impossible in practice. In this paper, we propose data-driven semi-definite programs to formally verify stability and safety for a neural network controlled linear system with unknown dynamics. The proposed method performs verification directly from end-to-end without identifying the dynamics. Through a numerical example, we validate the efficacy of our method on linear systems with controller trained by imitation learning.