用分段仿射函数和神经网络表示实际非光滑控制李雅普诺夫函数

IF 2.1 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2025-04-23 DOI:10.1016/j.sysconle.2025.106103

Lars Grüne , Mario Sperl , Debasish Chatterjee

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引用次数: 0

摘要

本文给出了控制李雅普诺夫函数存在的条件，该控制李雅普诺夫函数既可以用分段仿射函数表示，也可以用具有适当数目的ReLU层的神经网络表示。研究结果为基于优化和机器学习技术的控制李雅普诺夫函数的计算方法提供了理论基础。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Representation of practical nonsmooth control Lyapunov functions by piecewise affine functions and neural networks

In this paper we give conditions under which control Lyapunov functions exist that can be represented by either piecewise affine functions or by neural networks with a suitable number of ReLU layers. The results provide a theoretical foundation for recent computational approaches for computing control Lyapunov functions with optimization-based and machine-learning techniques.

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来源期刊

Systems & Control Letters 工程技术-运筹学与管理科学

CiteScore

4.60

自引率

3.80%

发文量

144

审稿时长

6 months

期刊介绍： Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.