Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

Discrete Geometry Approach to Structure-Preserving Discretization of Port-Hamiltonian Systems

Computers have emerged as essential tools in the modern scientific analysis and simulationbased design of complex physical systems. The deeply-seated abstraction of continuity immanent to many physical systems inherently clashes with a digital computer’s ability of storing and manipulating only finite sets of numbers. While there has been a number of computational techniques that proposed discr...

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...

Distributed-Parameter Port-Hamiltonian Systems

Discrete port-Hamiltonian systems

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling at the discrete level itself. One of the goals of this paper is to model port-Hamiltonian systems...

Structure preserving model reduction of port-Hamiltonian systems

It is shown that by use of the Kalman-decomposition an uncontrollable and/or unobservable port-Hamiltonian system is reduced to a controllable/observable system that inherits a port-Hamiltonian structure. Energy and co-energy variable representations for port-Hamiltonian systems are discussed and the reduction procedures are used for both representations. For a general portHamiltonian system in...