We discuss the modelling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control. The structure is ideal for automated network-based modelling 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 descriptor systems, we demonstrate that many difficulties that arise in general descriptor systems can be easily overcome within the port-Hamiltonian framework. The properties of port-Hamiltonian descriptor systems are analysed, and time discretization and numerical linear algebra techniques are discussed. Structure-preserving regularization procedures for descriptor systems are presented to make them suitable for simulation and control. Model reduction techniques that preserve the structure and stabilization and optimal control techniques are discussed.The properties of port-Hamiltonian descriptor systems and their use in modelling simulation and control methods are illustrated with several examples from different physical domains. The survey concludes with open problems and research topics that deserve further attention.

中文翻译：

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端口哈密顿微分代数系统的控制和应用

我们讨论了端口哈密顿描述符系统的建模框架及其在数值模拟和控制中的应用。该结构是基于网络的自动化建模的理想选择，因为它在节能互连、同余变换和伽辽金投影下是不变的。此外，稳定性和钝化特性很容易表现出来。正交变换下的凝聚形式为存在性、唯一性、规律性和数值方法提供了简单的分析工具来检查这些属性。在回顾了一般线性和非线性描述符系统的概念之后，我们证明了可以很容易地克服一般描述符系统中出现的许多困难在港口哈密顿框架内。分析了 port-Hamiltonian 描述符系统的属性，讨论了时间离散化和数值线性代数技术。介绍了描述符系统的结构保持正则化程序，使其适用于模拟和控制。讨论了保持结构和稳定性的模型简化技术以及最优控制技术。通过来自不同物理域的几个例子说明了端口哈密顿描述符系统的特性及其在建模仿真和控制方法中的应用。该调查以值得进一步关注的未解决问题和研究主题作为结尾。讨论了保持结构和稳定性的模型简化技术以及最优控制技术。通过来自不同物理域的几个例子说明了端口哈密顿描述符系统的特性及其在建模仿真和控制方法中的应用。该调查以值得进一步关注的未解决问题和研究主题作为结尾。讨论了保持结构和稳定性的模型简化技术以及最优控制技术。通过来自不同物理域的几个例子说明了端口哈密顿描述符系统的特性及其在建模仿真和控制方法中的应用。该调查以值得进一步关注的未解决问题和研究主题作为结尾。