On the relationship between stochastic and deterministic energy shaping techniques for stochastic port-Hamiltonian systems via invariant measure characterization

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

Automatica Pub Date : 2025-05-30 DOI:10.1016/j.automatica.2025.112385

Francesco Giuseppe Cordoni , Luca Di Persio , Riccardo Muradore

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引用次数: 0

Abstract

This paper derives two relevant results in the context of weak energy shaping for stochastic port-Hamiltonian systems (SPHS). Energy shaping is a technique systematically used to design feedback laws that shape the Hamiltonian of a controlled system to converge to a desired configuration under a general passivity condition. Such an approach has been recently extended to SPHS, but the resulting theory has limitations excluding relevant examples such as the additive noise case. However, it has been shown that the invariant measure of the SPHS allows the introduction of a weaker notion of convergence, hence obtaining a significant extension of the classical energy shaping theory for SPHS. In this paper, we continue investigating the weak energy shaping of SPHS, showing that the Fokker–Planck equation associated with an SPHS can be seen as the Fokker–Planck equation of an infinite-dimensional deterministic PHS. Moreover, we explicitly compute the invariant measure for a specific class of SPHS with additive noise.

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基于不变测度表征的随机端口-哈密顿系统随机与确定性能量整形技术之间的关系

本文在随机端口-哈密顿系统（SPHS）弱能量整形的背景下得到两个相关的结果。能量整形是一种系统地用于设计反馈定律的技术，该反馈定律使受控系统的哈密顿量在一般无源条件下收敛到期望的配置。这种方法最近已扩展到SPHS，但所得到的理论有局限性，排除了相关的例子，如加性噪声的情况。然而，研究表明，SPHS的不变测度允许引入较弱的收敛概念，从而对经典的SPHS能量塑造理论进行了重要的扩展。在本文中，我们继续研究了SPHS的弱能量整形，表明与SPHS相关的Fokker-Planck方程可以看作是无限维确定性小灵通的Fokker-Planck方程。此外，我们还显式地计算了一类具有加性噪声的特定SPHS的不变测度。

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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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.