用于建模与控制的N维端口哈密顿系统的Stokes-Lagrange和Stokes-Dirac表示
Stokes-Lagrange and Stokes-Dirac representations of $N$-dimensional port-Hamiltonian systems for modelling and control
AI总结：
本文引入Stokes-Lagrange结构扩展端口哈密顿框架，提出其通过满足分部积分公式的微分算子显式定义子空间的特性，经示例验证多等效表示存在，为系统建模与控制提供新工具。
摘要：
本文通过引入Stokes-Lagrange结构的概念扩展了端口哈密顿框架，该结构能够在N维域上隐式定义哈密顿量并将能量端口纳入系统。这一新框架与现有的Dirac和Stokes-Dirac结构相平行。我们提出Stokes-Lagrange结构作为一个特定情况，其中子空间通过满足分部积分公式的微分算子显式定义。通过从Stokes-Lagrange结构的视角研究各种示例，我们证明了多种等效系统表示的存在。这些表示为数值模拟和控制设计提供了显著优势，为端口哈密顿系统的建模与控制提供了额外工具。
英文摘要：
In this paper, we extend the port-Hamiltonian framework by introducing the concept of Stokes-Lagrange structure, which enables the implicit definition of a Hamiltonian over an $N$-dimensional domain and incorporates energy ports into the system. This new framework parallels the existing Dirac and Stokes-Dirac structures. We propose the Stokes-Lagrange structure as a specific case where the subspace is explicitly defined via differential operators that satisfy an integration by parts formula. By examining various examples through the lens of the Stokes-Lagrange structure, we demonstrate the existence of multiple equivalent system representations. These representations provide significant advantages for both numerical simulation and control design, offering additional tools for the modelling and control of port-Hamiltonian systems.
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