Multivalued Hamiltonian systems with sliding motions: Analysis of the backward-Euler discretisation

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2025-08-27 DOI:10.1016/j.automatica.2025.112567

Fernando Castaños , Félix Miranda-Villatoro , Bernard Brogliato

引用次数: 0

Abstract

This article is mainly concerned with the time-discretisation of multivalued Hamiltonian systems with multivalued dissipation, a special class of differential inclusions. Two classes of set-valued Hamiltonian systems are considered, depending on whether the dissipation function is position- or momentum-dependent. The backward-Euler discretisation is analysed in both cases: the well-posedness of the generalised equation obtained after discretisation is proved, and then finite-time stability of fixed points is tackled. The well-known twisting and super-twisting sliding-mode algorithms, as well as an example from Contact Mechanics and dynamical optimisation, illustrate the theoretical developments.

查看原文本刊更多论文

具有滑动运动的多值哈密顿系统：后向欧拉离散化分析

本文主要研究具有多值耗散的多值哈密顿系统的时间离散化问题，这是一类特殊的微分包含。根据耗散函数是位置相关还是动量相关，考虑了两类集值哈密顿系统。对这两种情况下的后向欧拉离散化进行了分析，证明了离散化后得到的广义方程的适定性，并讨论了不动点的有限时间稳定性问题。众所周知的扭转和超扭转滑模算法，以及接触力学和动态优化的一个例子，说明了理论的发展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.