The paper focuses on the stability analysis and control design for a general class of recurrent neural networks (RNNs). The key points are:
The authors consider a discrete-time RNN model with sigmoid nonlinearities that satisfy certain assumptions. This model represents various RNN families like Echo State Networks and Neural NARX networks.
For this RNN model, the authors first provide global exponential stability conditions based on a sector condition. However, these global conditions can be conservative.
To address this, the authors propose two different regional stability conditions based on linear matrix inequalities (LMIs).
The first regional condition combines a generalized sector condition with an auxiliary function that bounds the difference between the sigmoid and saturation nonlinearities.
The second regional condition uses a parametric sector condition that narrows the region of validity as a function of a design parameter.
The regional stability conditions are then used to design a state-feedback controller that ensures closed-loop stability and performance.
Numerical simulations are provided to illustrate the advantages and limitations of the proposed methods.
Overall, the paper presents novel LMI-based techniques for analyzing the regional stability of RNN-based control systems and leveraging this for controller design.
他の言語に翻訳
原文コンテンツから
arxiv.org
深掘り質問