Discrete-Time Models for Implicit Port-Hamiltonian Systems

TL;DR

This paper explores implicit finite-dimensional port-Hamiltonian systems, focusing on their use in numerical simulation and control, and presents methods to create structure-preserving sampled-data models from implicit representations.

Contribution

It introduces an implicit representation framework for port-Hamiltonian systems and demonstrates how to construct sampled-data models that maintain the original structure.

Findings

Implicit representations are effective for modeling in Cartesian coordinates.

Sampled-data models can preserve port-Hamiltonian structure.

The approach facilitates numerical simulation and control design.

Abstract

Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations (the system model is in a DAE form). Such representations lend themselves better to sample-data approximations. An implicit representation of a port-Hamiltonian system is given and it is shown how to construct a sampled-data model that preserves the port-Hamiltonian structure under sample and hold.