arXiv 2106.113662021-06-21eess.SYcs.SYmath.DSmath.OC

Adaptive Sampling for Structure Preserving Model Order Reduction of Port-Hamiltonian Systems

Paul Schwerdtner, Matthias Voigt

备注：: 6 pages, 4 figures

英文摘要：

We present an adaptive sampling strategy for the optimization-based structure preserving model order reduction (MOR) algorithm developed in [Schwerdtner, P. and Voigt, M. (2020). Structure preserving model order reduction by parameter optimization, Preprint arXiv:2011.07567]. This strategy reduces the computational demand and the required a priori knowledge about the given full order model, while at the same time retaining a high accuracy compared to other structure preserving but also unstructured MOR algorithms. A numerical study with a port-Hamiltonian benchmark system demonstrates the effectiveness of our method combined with its new adaptive sampling strategy. We also investigate the distribution of the sample points.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Structure-Preserving Model Order Reduction for Index One Port-Hamiltonian Descriptor Systems

We develop optimization-based structure-preserving model order reduction (MOR) methods for port-Hamiltonian (pH) descriptor systems of differentiation index one. Descriptor systems in pH form permit energy-based modeling and intuitive coupling of physical systems across different physical domains, scales, and accuracies. This makes pH models well-suited building-blocks for component-wise modeling of large system networks. In this context, it is often necessary to preserve the pH structure during MOR. We discuss current projection-based and structure-preserving MOR algorithms for pH systems and…

2022-06-02cs.SYeess.SYmath.DS

保持结构和稳定性的端口哈密顿系统学习

Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems

Department of Electrical and Computer Engineering, College of Engineering and Computer Science, University of Central Florida（电气与计算机工程系，工程与计算机科学学院，中央佛罗里达大学）

本文提出一种基于神经网络的端口哈密顿系统建模方法，通过放宽凸性约束提升模型表达能力，保留哈密顿结构和稳定性，通过实验验证其在保持结构和稳定性方面优于基线方法。

2026-04-14cs.LGcs.SYeess.SY

Structure preserving discontinuous Galerkin approximation of one-dimensional port-Hamiltonian systems

In this article, we present the structure-preserving discretization of linear one-dimensional port-Hamiltonian (PH) systems of two conservation laws using discontinuous Galerkin (DG) methods. We recall the DG discretization procedure which is based on a subdivision of the computational domain, an elementwise weak formulation with up to two integration by parts, and the interconnection of the elements using several numerical fluxes. We present the interconnection of the element models, which is power preserving in the case of conservative (unstabilized) numerical fluxes, and we set up the resul…

2022-12-16cs.SYeess.SY

Structure-preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems

We examine interpolatory model reduction methods that are well-suited for treating large scale port-Hamiltonian differential-algebraic systems in a way that is able to preserve and indeed, take advantage of the underlying structural features of the system. We introduce approaches that incorporate regularization together with prudent selection of interpolation data. We focus on linear time-invariant systems and present a systematic treatment of a variety of model classes that include combinations of index-$1$ and index-$2$ systems, describing in particular how constraints may be represented in …

2021-11-01cs.NAcs.SYeess.SY

超弹性弦的端口-哈密顿公式化与保结构离散化

Port-Hamiltonian formulation and structure-preserving discretization of hyperelastic strings

本文提出几何精确超弹性弦的端口-哈密顿表示，并利用保结构离散化（混合有限元和离散导数）构建有限维状态空间模型，实现能量一致仿真，支持控制设计。

2023-11-09cs.CEcs.SYeess.SY

Extended balancing of continuous LTI systems: a structure-preserving approach

In this paper, we treat extended balancing for continuous-time linear time-invariant systems, and we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model.

2020-01-02cs.SYeess.SYmath.OC

更多相关论文收起更多论文

Structure-Preserving Model Order Reduction for Index Two Port-Hamiltonian Descriptor Systems

We present a new optimization-based structure-preserving model order reduction (MOR) method for port-Hamiltonian descriptor systems (pH-DAEs) with differentiation index two. Our method is based on a novel parameterization that allows us to represent any linear time-invariant pH-DAE with a minimal number of parameters, which makes it well-suited to model reduction. We propose two algorithms which directly optimize the parameters of a reduced model to approximate a given large-scale model with respect to either the H-infinity or the H-2 norm. This approach has several benefits. Our parameterizat…

2022-06-08cs.NAcs.SYeess.SY

基于端粒杆动力学的混合公式与结构保持离散化：在端粒-哈密顿框架中

Mixed formulation and structure-preserving discretization of Cosserat rod dynamics in a port-Hamiltonian framework

Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）；Eindhoven University of Technology (TU/e)（埃因霍温理工大学）

本文提出基于能量的端粒杆动力学建模框架，采用混合公式与结构保持离散化，在端粒-哈密顿框架中实现非线性动力学，通过有限旋转表示与能量-动量一致积分方案，整合耗散材料行为与非标准驱动方法。

2026-02-27cs.CEcs.NAcs.RO

Dual field structure-preserving discretization of port-Hamiltonian systems using finite element exterior calculus

In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present a finite element exterior calculus formulation that is able to mimetically represent conservation laws and cope with mixed open boundary conditions using a single computational mesh. The possibility of including open boundary conditions allows for modular composition of complex multi-physical systems whereas the exterior calculus formulation provides a coordinate-free treatment. Our approach relies on a dual-field representation of the physical system th…

2022-08-02cs.NAcs.SYeess.SY

弱形式的斯托克斯-狄拉克结构与端口哈密顿系统几何离散化

Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems

Université Claude Bernard Lyon 1（里昂第一大学）；Technical University of Munich（慕尼黑工业大学）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）

本文提出分布式参数端口哈密顿系统的混合伽辽金离散化方法，通过超几何守恒律系统示例，推导了弱形式的几何斯托克斯-狄拉克结构、有限维狄拉克结构的几何近似以及一致哈密顿量近似，实现了结构保持的有限维端口哈密顿状态空间模型。

2018-02-28cs.NAcs.SYeess.SY

边界控制一维端口哈密顿系统的保结构离散化与模型降阶

Structure-Preserving Discretization and Model Order Reduction of Boundary-Controlled 1D Port-Hamiltonian Systems

本文针对边界控制端口哈密顿系统提出基于分区有限元法的保结构离散化方案，并结合Loewner框架实现保被动的模型降阶，通过投影算子恢复状态变量物理意义，以波动方程和Timoshenko梁验证方法通用性。

2024-07-01cs.NAcs.SYeess.SY

Event-triggered Control of Port-Hamiltonian Systems under Time-delay Communication

We study the problem of periodic event-triggered control of interconnected port-Hamiltonian systems subject to time-varying delays in their communication. In particular, we design a threshold parameter for the event-triggering condition, a sampling period, and a maximum allowable delay such that interconnected port-Hamiltonian control systems with periodic event-triggering mechanism under a time-delayed communication are able to achieve asymptotically stable behaviour. Simulation results are presented to validate the theory.

2022-07-13cs.SYeess.SY

基于高斯过程的端口哈密顿DAE系统的数据驱动辨识

Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes

University of Wuppertal（伍珀塔尔大学）；School of Mathematics and Natural Sciences（数学与自然科学学院）；IMACM

本研究提出基于高斯过程的端口哈密顿微分代数方程（pH-DAE）系统数据驱动辨识方法，利用输入和状态数据估计非线性作用力函数，突破了现有仅能辨识常微分方程系统的局限，并成功应用于网络设计与多体动力学场景。

2024-06-26cs.LGcs.NAcs.SY

A Rosenbrock framework for tangential interpolation of port-Hamiltonian descriptor systems

We present a new structure-preserving model order reduction (MOR) framework for large-scale port-Hamiltonian descriptor systems (pH-DAEs). Our method exploits the structural properties of the Rosenbrock system matrix for this system class and utilizes condensed forms which often arise in applications and reveal the solution behaviour of a system. Provided that the original system has such a form, our method produces reduced-order models (ROMs) of minimal dimension, which tangentially interpolate the original model's transfer function and are guaranteed to be again in pH-DAE form. This allows t…

2022-10-28cs.NAcs.SYeess.SY

N维环境下传导-扩散作为不可逆端口哈密顿系统

Conduction-Diffusion in N-Dimensional settings as irreversible port-Hamiltonian systems

University of Waterloo（滑铁卢大学）；Université Marie et Louis Pasteur, SUPMICROTECH, CNRS, institut FEMTO-ST（玛丽和路易·巴斯德大学、SUPMICROTECH、法国国家科学研究中心、FEMTO-ST研究所）；Universidad Tecnica Federico Santa Maria（费德里科·圣塔玛丽亚理工大学）；Fédération ENAC ISAE-SUPAERO ONERA, Université de Toulouse（ENAC ISAE-SUPAERO ONERA联盟、图卢兹大学）

本文提出了一种适用于N维环境的传导-扩散现象的不可逆端口哈密顿系统模型，为多物理过程的系统建模与控制提供了理论基础。

2026-03-11cs.SYeess.SY

基于能量的混合模型用于物理AI：可证明稳定的端哈密顿动力学识别

Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics

RIAS Lab The Italian Institute of Artificial Intelligence for Industry（意大利人工智能工业研究所 RIAS 实验室）；Delft Center for Systems and Control, TU Delft（代尔夫特理工大学代尔夫特系统与控制中心）

本文提出一种混合能量模型框架，用于系统识别，通过可证明稳定的耗散吸收不变动态，扩展了能量模型理论，验证了端哈密顿能量模型的稳定性与安全性。

2026-04-02cs.AIcs.LGcs.SY

端口哈密顿系统积分控制：无坐标变换的非被动输出

Integral control of port-Hamiltonian systems: non-passive outputs without coordinate transformation

The University of Newcastle（纽卡斯尔大学）；University of Naples Federico II（那不勒斯费德里科二世大学）

本文提出一种为端口哈密顿系统非被动输出添加积分作用的方法，通过动态扩展保持系统形式，能抑制匹配和非匹配扰动，且无需坐标变换。

2017-03-23cs.SYeess.SY