论文标题
控制哈米尔顿港的差分 - 代数系统和应用
Control of port-Hamiltonian differential-algebraic systems and applications
论文作者
论文摘要
讨论了哈米尔顿港描述符系统的建模框架及其在数值模拟和控制中的使用。该结构是基于自动网络的建模的理想选择，因为它在电力强调互连，一致性转换和Galerkin投影下是不变的。此外，稳定性和被动性属性很容易显示。正交转换下的凝结形式提出了简单的分析工具，用于检查这些属性的存在，独特性，规律性和数值方法。 在回顾了通用线性和非线性描述符系统的概念之后，我们证明了在哈米尔顿港框架内很容易克服一般描述符系统中出现的许多困难。分析了哈米尔顿港描述器系统的特性，时间消化，并讨论了数值线性代数技术。提出了描述符系统的结构保护正则化程序，以使其适合模拟和控制。讨论了保留结构和稳定和最佳控制技术的模型还原技术。 使用来自不同物理域的几个示例，用来说明了哈米尔顿港描述符系统的属性及其在建模模拟和控制方法中的使用。该调查以开放问题和研究主题的结尾，应受到进一步关注。
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 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 analyzed, 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 modeling 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.
