On an intrinsic formulation of time-variant Port Hamiltonian systems

TL;DR

This paper introduces an intrinsic, coordinate-invariant formulation of time-variant Port Hamiltonian systems using covariant derivatives, enhancing modeling and control analysis for time-dependent systems.

Contribution

It presents a novel intrinsic formulation based on splitting the state bundle and covariant derivatives, applicable to control problems and time-variant error systems.

Findings

Invariant structure under time-variant coordinate transformations

Application to trajectory tracking error systems

Analysis of power flow balancing in an intrinsic framework

Abstract

In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate covariant derivatives, which guarantees that the structure of the equations is invariant with respect to time-variant coordinate transformations. In particular, we will interpret our covariant system representation in the context of control theoretic problems. Typical examples are time-variant error systems related to trajectory tracking problems which allow for a Hamiltonian formulation. Furthermore we will analyze the concept of collocation and the balancing/interaction of power flows in an intrinsic fashion.