A port-Hamiltonian approach to modeling and interconnections of canal systems

We show how the port-Hamiltonian formulation of distributed parameter systems, which incorporates energy flow through the boundary of the spatial domain of the system, can be used to model networks of canals and study interconnections of such systems. We first formulate fluid flow with 1-d spatial variable whose dynamics are given by the well-known shallow water equations, with respect to a Stokes-Dirac structure, and then consider a slightly more complicated case where we have a modified (a non-constant) Stokes-Dirac structure. We also explore the existence of Casimir functions for such systems and highlight their implications on control of fluid dynamical systems.

A Finite Dimensional Approximation of the shallow water Equations: The port-Hamiltonian Approach

We look into the problem of approximating a distributed parameter port-Hamiltonian system which is represented by a non-constant Stokes-Dirac structure. We here employ the idea where we use different finite elements for the approximation of geometric variables (forms) describing a infinite-dimensional system, to spatially discretize the system and obtain a finite-dimensional port-Hamiltonian system. In particular we take the example of a special case of the shallow water equations.

On interconnections of infinite-dimensional port-Hamiltonian systems

Network modeling of complex physical systems leads to a class of nonlinear systems called port-Hamiltonian systems, which are defined with respect to a Dirac structure (a geometric structure which formalizes the power-conserving interconnection structure of the system). A power conserving interconnection of Dirac structures is again a Dirac structure. In this paper we study interconnection properties of mixed finite and infinite dimensional port-Hamiltonian systems and show that this interconnection again defines a port-Hamiltonian system. We also investigate which closed-loop port-Hamiltonian systems can be achieved by power conserving interconnections of finite and infinite dimensional port-Hamiltonian systems. Finally we study these results with particular reference to the transmission line