Hamiltonian formulation of distributed-parameter systems with boundary energy flow

Distributed-Parameter Port-Hamiltonian Systems

Portcontrolled Hamiltonian representation of distributed parameter systems

A port controlled Hamiltonian formulation of the dynamics of distributed parameter systems is presented, which incorporates the energy flow through the boundary of the domain of the system, and which allows to represent the system as a boundary control Hamiltonian system. This port controlled Hamiltonian system is defined with respect to a Dirac structure associated with the exterior derivative...

a Simplified Model of Distributed Parameter Systems

A generalized simplified model for describing the dynamic behavior of distributed parameter systems is proposed. The various specific characteristics of gain and phase angle of distributed parameter systems are investigated from frequency response formulation and complex plane representation of the proposed simplified model. The complex plane investigation renders some important inequality cons...

Explicit Simplicial Discretization of Distributed-Parameter Port-Hamiltonian Systems

Simplicial Dirac structures as finite analogues of the canonical Stokes-Dirac structure, capturing the topological laws of the system, are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators. These finite-dimensional Dirac structures offer a framework for the formulation of standard input-output finite-dimensional portHamiltonian systems that...

Energy shaping of boundary controlled linear port Hamiltonian systems

In this paper, we consider the asymptotic stabilization of a class of one dimensional boundary controlled port Hamiltonian systems by an immersion/reduction approach and the use of Casimir invariants. We first extend existing results on asymptotic stability of linear infinite dimensional systems controlled at their boundary to the case of stable Port Hamiltonian controllers including some physi...