154 research outputs found
On the port-Hamiltonian representation of systems described by partial differential equations
We consider infinite dimensional port-Hamiltonian systems. Based on a power
balance relation we introduce the port-Hamiltonian system representation where
we pay attention to two different scenarios, namely the non-differential
operator case and the differential operator case regarding the structural
mapping, the dissipation mapping and the in/output mapping. In contrast to the
well-known representation on the basis of the underlying Stokes-Dirac structure
our approach is not necessarily based on using energy-variables which leads to
a different port-Hamiltonian representation of the analyzed partial
differential equations.Comment: A definitive version has been published in ifac-papersonline.ne
Port Hamiltonian Formulation of Infinite Dimensional Systems II. Boundary Control by Interconnection
On Power Balancing and Stabilization for a Class of infinite-dimensional systems
In this paper we present control of infinite-dimensional systems by power
shaping methods, which have been used extensively for control of finite
dimensional systems. Towards achieving the results we work within the Brayton
Moser framework, by using the system of transmission line as an example and
derive passivity of the system with respect to the boundary voltages and
derivatives of current at the boundary. We then solve the stabilization problem
by interconnecting the system through a finite-dimensional controller and
generating Casimirs for the closed-loop system. Finally we explore possibility
of generating other alternate passive maps.Comment: The 21st International Symposium on Mathematical Theory of Networks
and Systems (MTNS 2014
Hamiltonian Coupling of Electromagnetic Field and Matter
Reversible part of evolution equations of physical systems is often generated
by a Poisson bracket. We discuss geometric means of construction of Poisson
brackets and their mutual coupling (direct, semidirect and matched-pair
products) as well as projections of Poisson brackets to less detailed Poisson
brackets. This way the Hamiltonian coupling between transport of mixtures and
electrodynamics is elucidated
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.
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