Validation of Neural Network Controllers for Uncertain Systems Using the Keep‐Close Approach: Robustness Analysis and Safety Verification

ABSTRACT The safety verification of neural network (NN) controllers operating in uncertain environments characterized by unmodeled dynamics, nonlinearities, and time delays remains a fundamental challenge in robust control analysis. This article introduces a novel method, termed Keep‐Close , for analyzing the performance and robustness of uncertain feedback systems equipped with NN controllers. The proposed framework formulates the problem as an analysis of the dynamical deviation between an NN‐controlled uncertain system and a robust reference model. First, the behavior of the NN controller is characterized using the Differential Mean Value Theorem (DMV) and linear approximation techniques. A new dynamical system is then constructed to describe this deviation, enabling worst‐case analysis of the Relative Integral Square Error (RISE) and the Supreme Square Error (SSE) through the combined use of Integral Quadratic Constraints (IQCs) and Lyapunov theory. The effectiveness of the proposed approach is demonstrated through two case studies, namely the Single‐Link Robot Arm and the Apollo Lander, highlighting its versatility and capability in assessing the robustness and performance of NN controllers in complex and uncertain environments.