Stability Analysis of Recurrent Neural Networks by IQC with Copositive Mutipliers

Yoshio Ebihara, Hayato Waki, Victor Magron, Ngoc Hoang Anh Mai, DImitri Peaucelle, Sophie Tarbouriech

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

抄録

This paper is concerned with the stability analysis of the recurrent neural networks (RNNs) by means of the integral quadratic constraint (IQC) framework. The rectified linear unit (ReLU) is typically employed as the activation function of the RNN, and the ReLU has specific nonnegativity properties regarding its input and output signals. Therefore, it is effective if we can derive IQC-based stability conditions with multipliers taking care of such nonnegativity properties. However, such nonnegativity (linear) properties are hardly captured by the existing multipliers defined on the positive semidefinite cone. To get around this difficulty, we loosen the standard positive semidefinite cone to the copositive cone, and employ copositive multipliers to capture the nonnegativity properties. We show that, within the framework of the IQC, we can employ copositive multipliers (or their inner approximation) together with existing multipliers such as Zames-Falb multipliers and polytopic bounding multipliers, and this directly enables us to ensure that the introduction of the copositive multipliers leads to better (no more conservative) results. We finally illustrate the effectiveness of the IQC-based stability conditions with the copositive multipliers by numerical examples.

本文言語英語
ホスト出版物のタイトル60th IEEE Conference on Decision and Control, CDC 2021
出版社Institute of Electrical and Electronics Engineers Inc.
ページ5098-5103
ページ数6
ISBN(電子版)9781665436595
DOI
出版ステータス出版済み - 2021
イベント60th IEEE Conference on Decision and Control, CDC 2021 - Austin, 米国
継続期間: 12月 13 202112月 17 2021

出版物シリーズ

名前Proceedings of the IEEE Conference on Decision and Control
2021-December
ISSN(印刷版)0743-1546

会議

会議60th IEEE Conference on Decision and Control, CDC 2021
国/地域米国
CityAustin
Period12/13/2112/17/21

!!!All Science Journal Classification (ASJC) codes

  • 制御およびシステム工学
  • モデリングとシミュレーション
  • 制御と最適化

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