提出一种分析带神经网络反馈的正系统鲁棒稳定性的新方法。
Robust Stability Analysis of Positive Lure System with Neural Network Feedback
- 利用正系统特性推导出Lur'e系统的稳定性半径公式。
- 在参数不确定和非线性界未知条件下实现鲁棒稳定分析。
- 适用于含神经网络的复杂控制系统，适合控制理论研究者。
本文研究在正性约束下Lur'e问题的鲁棒性，基于正Aizerman猜想和Metzler矩阵的鲁棒性结论。考虑一类具有参数不确定性和未知非线性扇区界的Lur'e型控制系统，通过正线性系统工具，有效处理复杂不确定性非线性系统。利用系统正性特征，推导出Lur'e系统稳定性半径的显式公式。进一步将分析扩展至带神经网络（NN）反馈的系统，并提出一种改进神经网络扇区界的方法。该研究提供了一种可扩展、高效的鲁棒性分析框架，适用于Lur'e系统及神经网络控制的系统。最后通过示例验证了所提结果的有效性。
原文摘要 · Abstract (English)
This paper investigates the robustness of the Lur'e problem under positivity constraints, drawing on results from the positive Aizerman conjecture and robustness properties of Metzler matrices. Specifically, we consider a control system of Lur'e type in which not only the linear part includes parametric uncertainty but also the nonlinear sector bound is unknown. We investigate tools from positive linear systems to effectively solve the problems in complicated and uncertain nonlinear systems. By leveraging the positivity characteristic of the system, we derive an explicit formula for the stability radius of Lur'e systems. Furthermore, we extend our analysis to systems with neural network (NN) feedback loops. Building on this approach, we also propose a refinement method for sector bounds of NNs. This study introduces a scalable and efficient approach for robustness analysis of both Lur'e and NN-controlled systems. Finally, the proposed results are supported by illustrative examples.
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