Port-Hamiltonian system theory is a well-known framework for the control of complex physical systems. The majority of port-Hamiltonian control design methods base on an explicit input-state-output port-Hamiltonian model for the system under consideration. However in the literature, little effort has been made towards a systematic, automatable derivation of such explicit models. In this paper, we present a constructive, formally rigorous method for an explicit port-Hamiltonian formulation of multi-bond graphs. Two conditions, one necessary and one sufficient, for the existence of an explicit port-Hamiltonian formulation of a multi-bond graph are given. We summarise our approach in an algorithm for the automated generation of an explicit port-Hamiltonian model from a given multi-bond graph. An academic example illustrates the results of this paper.

哈密​​顿系统理论是控制复杂物理系统的著名框架。大多数港口-哈密顿控制设计方法都基于明确的所考虑系统的输入-状态-输出端口-哈密尔顿模型。但是，在文献中，对于这种显式模型的系统化，自动化的推导工作很少。在本文中，我们为多键图的显式Port-Hamiltonian表示法提供了一种结构严谨，形式严谨的方法。对于存在多键图的明确的端口-哈密尔顿公式，给出了两个条件，一个必要条件和一个充分条件。我们在一种算法中总结了我们的方法，该算法可根据给定的多键图自动生成显式端口-哈密顿模型。一个学术例子说明了本文的结果。