Alexandre Anahory Simoes, David Martín de Diego, Bernhard Maschke
In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.
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There has been considerable interest in designing Markov chain Monte Carlo algorithms by exploiting numerical methods for Langevin dynamics, which includes Hamiltonian dynamics as a deterministic case. A prominent approach is Hamiltonian Monte Carlo (HMC), where a leapfrog discretization of Hamiltonian dynamics is employed. We investigate a recently proposed class of irreversible sampling algorithms, called Hamiltonian assisted Metropolis sampling (HAMS), which uses an augmented target density similarly as in HMC, but involves a flexible proposal scheme and a carefully formulated acceptance-re…
Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within dynamic iteration procedures. To this end, we introduce new classes of port-Hamiltonian differential-algebraic equations. Thereby, we additionally allow for nonlinear dissipation on a subspace of the state space. Both, each subsystem and the overall system, possess a port-Hamiltonian structure. A structural analysis is performed for the new setups. Dynamic iterati…
A port-Hamiltonian (pH) system formulation is a geometrical notion used to formulate conservation laws for various physical systems. The distributed parameter port-Hamiltonian formulation models infinite dimensional Hamiltonian dynamical systems that have a non-zero energy flow through the boundaries. In this paper we propose a novel framework for discontinuous Galerkin (DG) discretizations of pH-systems. Linking DG methods with pH-systems gives rise to compatible structure preserving finite element discretizations along with flexibility in terms of geometry and function spaces of the variable…
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian Systems
针对大规模多输入多输出端口哈密顿系统，提出通过切向有理插值进行模型降阶，所得降阶模型保持端口哈密顿结构且无源，并引入基于H2最优的算法选择插值点与切向方向。
Port-Hamiltonian Realizations of Nonminimal Linear Time Invariant Systems
本文研究了非最小线性时不变系统的端哈密顿表示方法，提出了一种能处理反馈项不可逆情况的构造方法，并通过数值实验验证了其有效性。
Model reduction techniques for linear constant coefficient port-Hamiltonian differential-algebraic systems
针对多物理问题导出的高维线性常系数端口哈密顿微分代数系统，通过调整Dirac结构降阶和矩匹配两类技术，实现了保持结构和约束不变的模型降阶，并在流动与机械基准示例中验证了性能。
Energy-stable Port-Hamiltonian Systems
本文提出能量稳定端口-Hamiltonian（espH）系统，通过为能量稳定系统加入输入-输出端口形成pH表述，使其在时空离散化与模型降阶中保持结构。
We present a gradient-based calibration algorithm to identify a port-Hamiltonian system from given time-domain input-output data. The gradient is computed with the help of sensitivities and the algorithm is tailored such that the structure of the system matrices of the port-Hamiltonian system (skew-symmetry and positive semi-definiteness) is preserved in each iteration of the algorithm. As we only require input-output data, we need to calibrate the initial condition of the internal state of the port-Hamiltonian system as well. Numerical results with synthetic data show the feasibility of the a…
The port-Hamiltonian modelling framework allows for models that preserve essential physical properties such as energy conservation or dissipative inequalities. If all subsystems are modelled as port-Hamiltonian systems and the inputs are related to the output in a linear manner, the overall system can be modelled as a port-Hamiltonian system (PHS), too, which preserves the properties of the underlying subsystems. If the coupling is given by a skew-symmetric matrix, as usual in many applications, the overall system can be easily derived from the subsystems without the need of introducing dummy …
Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and port-Hamiltonian systems has been carried out. In this paper we demonstrate how existing methods can be employed to discretize dynamical plate problems in a structure-preserving way. Based on convergence results of existing schemes, new error estimates are conjectured; numerical simulations confirm the expected behaviors.
A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular applicable to port-Hamiltonian formulations arising from domain decompositions.
This paper contributes with a new formal method of spatial discretization of a class of nonlinear distributed parameter systems that allow a port-Hamiltonian representation over a one dimensional manifold. A specific finite dimensional port-Hamiltonian element is defined that enables a structure preserving discretization of the infinite dimensional model that inherits the Dirac structure, the underlying energy balance and matches the Hamiltonian function on any, possibly nonuniform mesh of the spatial geometry.
Structure-preserving Model Reduction for Nonlinear Port-Hamiltonian Systems
本文提出一种适用于大规模非线性端哈密顿系统的保持结构模型降维方法，通过保持端哈密顿结构确保降维模型的稳定性和被动性，并提供状态变量和输出的先验误差界。
This article presents a simple port-Hamiltonian formulation of the equations for an RLC electric circuit as a differential-algebraic equation system, and a proof that structural analysis always succeeds on it for a well-posed circuit, thus providing a correct regularisation for numerical solution. The DAE is small - its number of variables/equations is at most the number of edges in the circuit graph.
Moving-Boundary Port-Hamiltonian Systems
本文研究时变空间域上的线性边界端口哈密顿系统，推导其时变 Dirac 结构并建立新系统类，进而开发了动态网格空间离散化方案以近似求解时变域上的电报方程。
When computing the eigenstructure of matrix pencils associated with the passivity analysis of perturbed port-Hamiltonian descriptor system using a structured generalized eigenvalue method, one should make sure that the computed spectrum satisfies the symmetries that corresponds to this structure and the underlying physical system. We perform a backward error analysis and show that for matrix pencils associated with port-Hamiltonian descriptor systems and a given computed eigenstructure with the correct symmetry structure there always exists a nearby port-Hamiltonian descriptor system with exac…
Operator Splitting Based Dynamic Iteration for Linear Port-Hamiltonian Systems
本文针对线性微分代数端口哈密顿系统提出一种基于Lions-Mercier型算子分裂的动态迭代方法，具有误差单调递减且无需稳定性条件的优点，并成功应用于多体系统与电气网络。
Structure-preserving discretization for port-Hamiltonian descriptor systems
本文研究了端口哈密顿描述系统的结构保持离散化方法，探讨了其在自动建模中的应用，并通过数值例子验证了在特定哈密顿函数假设下，某些方法能保持结构。
Port-Hamiltonian Realizations of Positive Real Descriptor Systems
本文研究了端口哈密顿系统与正实描述符系统的关系，改进了已有充分条件，针对完全可控、可观测且正实的描述符系统提出了充要条件及计算其端口哈密顿实现的显式方法。
Discrete-Time Models for Implicit Port-Hamiltonian Systems
研究隐式端口哈密顿系统在数值模拟和控制设计中的应用，提出保持端口哈密顿结构的采样模型方法。
Port-Hamiltonian systems theory provides a systematic methodology for the modeling, simulation and control of multi-physics systems. The incorporation of algebraic constraints has led to a multitude of definitions of port-Hamiltonian differential-algebraic equations (DAE) systems. This paper presents extensions of results in Gernandt, Haller & Reis (2021) and Mehrmann & Van der Schaft (2022) in the context of maximally monotone structures and shows that any such space can be written as composition of a Dirac and a resistive structure. Furthermore, appropriate coordinate representations are pre…
The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving interconnection, congruence transformations, and Galerkin projection. Moreover, stability and passivity properties are easily shown. Condensed forms under orthogonal transformations present easy analysis tools for existence, uniqueness, regularity, and numerical methods to check these properties. After recalling the concepts for general linear and nonlinear descript…
Energy-Preserving and Passivity-Consistent Numerical Discretization of Port-Hamiltonian Systems
本文系统设计了两种离散端口哈密顿系统，通过离散梯度方法和分裂方法，使系统满足离散被动性，从而通过适当选择输入使其全局渐近稳定。数值实验显示其性能优于现有相同阶次的积分器。
Goal-Oriented Time Adaptivity for Linear Port-Hamiltonian Differential-Algebraic Equations of Index~1
本文提出利用后验网格细化技术，通过双权重残差法控制端口哈密顿微分代数方程的能量平衡误差，利用耗散性利用的块雅可比近似高效计算误差估计器，通过电气电路模型仿真验证方法有效性。
Operator splitting for port-Hamiltonian systems
本文针对port-Hamiltonian系统提出一种算子分裂方法，将能量保守与耗散部分分开处理，以利用迭代矩阵特殊结构及多速率潜力，并通过耦合多体系统动力学示例验证。
Optimal robustness of port-Hamiltonian systems
本文研究了如何构造给定有理传递函数的最优鲁棒端口哈密顿实现，证明最大被动半径的实现是标准化的端口哈密顿系统，并提供了计算该解的算法，同时考虑了寻找最接近给定非被动系统的被动系统的近似解。
Discretization of Dirac systems and port-Hamiltonian systems: the role of the constraint algorithm
本文利用流形上的收缩与离散化映射研究Dirac结构离散化，并将其用于端口Hamilton系统数值积分器，同时探讨离散化与隐式微分方程约束算法的融合。
Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically known to be highly pessimistic in the sense of largely overestimating the true error. This work applies two improved error bounding techniques, namely (a) a hierarchical error bound and (b) an error bound based on an auxiliary linear problem, to the case of port-Hamiltonian systems. The approaches rely on a second approximation of (a) the dynamical system a…
Data-driven port-Hamiltonian structured identification for non-strictly passive systems
本研究针对非严格无源系统，基于频域数据改进现有方法构建保留端口哈密顿结构的降阶模型，解决Loewner框架应用于复杂构型的数值问题，并通过二维波动方程验证方案有效性。
Discretization of the Burgers' equation as a port-Hamiltonian system
本文提出端口哈密顿系统框架，用于处理Burgers方程的数值模拟，通过引入粘性项缓解间断处的伪振荡问题，并分析时间步长、空间分辨率与粘性参数的关系。
Discrete gradient methods for port-Hamiltonian differential-algebraic equations
本文提出了一种用于端哈密顿微分代数方程的离散梯度方法，通过结构保持方法解决非线性物理系统建模问题，并展示了其在多体动力学中的应用效果。
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