Port-Hamiltonian descriptor systems

TL;DR

This paper extends port-Hamiltonian systems to include constrained descriptor systems, providing a new invariant structure that aids in modeling, regularization, and simulation of high-index systems, demonstrated through examples.

Contribution

It introduces a novel algebraic and geometric port-Hamiltonian structure for descriptor systems, invariant under transformations, suitable for high-index systems and regularization.

Findings

New invariant port-Hamiltonian structure for descriptor systems

Modified regularization procedure for high-index systems

Demonstrated effectiveness with multiple examples

Abstract

The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is derived. It is shown that this structure is invariant under equivalence transformations, and that it is adequate also for the modeling of high-index descriptor systems. The regularization procedure for descriptor systems to make them suitable for simulation and control is modified to deal with the port-Hamiltonian structure. The relevance of the new structure is demonstrated with several examples.