利用神经网络控制器的扇区约束非线性确保系统的正向性和稳定性

IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS IEEE Control Systems Letters Pub Date : 2024-06-18 DOI:10.1109/LCSYS.2024.3416237
Hamidreza Montazeri Hedesh;Milad Siami
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引用次数: 0

摘要

这封信介绍了一种新方法,用于分析使用一类全连接前馈神经网络(FFNN)控制器的正反馈系统的稳定性。通过建立无偏全连接 FFNN 的扇区边界,我们提出了一个稳定性定理,证明了线性系统在全连接 FFNN 控制下的全局指数稳定性。利用正 Lur'e 系统和正 Aizerman 猜想的原理,我们的方法有效地解决了确保高度非线性系统稳定性的难题。我们方法的关键在于保持扇形边界,从而维护整个 Lur'e 系统的正向性和 Hurwitz 特性。我们通过在一个线性系统中实施我们的方法,该系统由一个根据输出反馈控制器数据训练的 FFNN 管理,从而展示了我们方法的实际应用性,突出了它在增强动态系统稳定性方面的潜力。
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Ensuring Both Positivity and Stability Using Sector-Bounded Nonlinearity for Systems With Neural Network Controllers
This letter introduces a novel method for the stability analysis of positive feedback systems with a class of fully connected feedforward neural networks (FFNN) controllers. By establishing sector bounds for fully connected FFNNs without biases, we present a stability theorem that demonstrates the global exponential stability of linear systems under fully connected FFNN control. Utilizing principles from positive Lur’e systems and the positive Aizerman conjecture, our approach effectively addresses the challenge of ensuring stability in highly nonlinear systems. The crux of our method lies in maintaining sector bounds that preserve the positivity and Hurwitz property of the overall Lur’e system. We showcase the practical applicability of our methodology through its implementation in a linear system managed by a FFNN trained on output feedback controller data, highlighting its potential for enhancing stability in dynamic systems.
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来源期刊
IEEE Control Systems Letters
IEEE Control Systems Letters Mathematics-Control and Optimization
CiteScore
4.40
自引率
13.30%
发文量
471
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