An Incremental Input-to-State Stability Condition for a Class of Recurrent Neural Networks

• 成果类型: Article
• 署名作者: D'Amico, William; La Bella, Alessio; Farina, Marcello
• 署名单位: Polytechnic University of Milan
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3327937
• 发表日期: 2024
• 页码: 2221-2236
• 关键词: Control systems; Stability criteria; Recurrent neural networks; asymptotic stability; Artificial neural networks; Symmetric matrices; Feedforward systems; Linear matrix inequalities; neural networks (NNs); nonlinear control systems; stability of nonlinear systems

摘要

This article proposes a novel sufficient condition for the incremental input-to-state stability of a class of recurrent neural networks (RNNs). The established condition is compared with others available in the literature, showing to be less conservative. Moreover, it can be applied for the design of incremental input-to-state stable RNN-based control systems, resulting in a linear matrix inequality constraint for some specific RNN architectures. The formulation of nonlinear observers for the considered system class, as well as the design of control schemes with explicit integral action, are also investigated. The theoretical results are validated through simulation on a referenced nonlinear system.