On an intrinsic formulation of time-variant Port Hamiltonian systems

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. NOTICE: this is the authors version of a work that was accepted for publication in Automatica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Automatica, Volume 48, Issue 9, September 2012, Pages 2194-2200 http://dx.doi.org/10.1016/j.automatica.2012.06.014,