City Research Online

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.

Publication Type:	Article
Additional Information:	© 2026 The Author(s). International Journal of Robust and Nonlinear Control published by John Wiley & Sons Ltd. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Publisher Keywords:	IQCs, Lyapunov, NN controller, robustness analysis, safety and verification
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science T Technology > TJ Mechanical engineering and machinery T Technology > TK Electrical engineering. Electronics Nuclear engineering T Technology > TL Motor vehicles. Aeronautics. Astronautics
Departments:	School of Science & Technology School of Science & Technology > Department of Engineering
SWORD Depositor:	Symplectic Administrator

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