Nonlinear Feedback, Double-bracket Dissipation and Port Control of Lie–Poisson Systems

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Nonlinear Science Pub Date : 2024-04-05 DOI:10.1007/s00332-024-10031-9

Simon Hochgerner

引用次数: 0

Abstract

Methods from controlled Lagrangians, double-bracket dissipation and interconnection and damping assignment–passivity-based control (IDA-PBC) are used to construct nonlinear feedback controls which (asymptotically) stabilize previously unstable equilibria of Lie–Poisson Hamiltonian systems. The results are applied to find an asymptotically stabilizing control for the rotor driven satellite, and a stabilizing control for Hall magnetohydrodynamic flow.

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Lie-Poisson 系统的非线性反馈、双支架耗散和端口控制

利用受控拉格朗日、双支架耗散和互联以及阻尼分配-基于传递性的控制（IDA-PBC）等方法构建非线性反馈控制，（渐近地）稳定先前不稳定的李-泊松哈密顿系统的平衡。研究结果被应用于为转子驱动卫星找到渐近稳定控制，以及为霍尔磁流体流找到稳定控制。

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

Journal of Nonlinear Science 数学-力学

CiteScore

5.00

自引率

3.30%

发文量

审稿时长

4.5 months

期刊介绍： The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be. All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.