On Casimir Functionals for Infinite-Dimensional Port-Hamiltonian Control Systems

Author

Schoberl, Markus ; Siuka, Andreas

Author_Institution

Inst. of Autom. Control & Control Syst. Technol., Univ. of Linz, Linz, Austria

Volume

58

Issue

7

fYear

2013

fDate

41456

Firstpage

1823

Lastpage

1828

Abstract

We consider infinite-dimensional port-Hamiltonian systems with respect to control issues. In contrast to the well-established representation relying on Stokes-Dirac structures that are based on skew-adjoint differential operators and the use of energy variables, we employ a different port-Hamiltonian framework. Based on this system representation conditions for Casimir functionals will be derived where in this context the variational derivative plays an extraordinary role. Furthermore the coupling of finite- and infinite-dimensional systems will be analyzed in the spirit of the control by interconnection problem.

Keywords

Casimir effect; differential geometry; interconnected systems; multidimensional systems; power control; variational techniques; Casimir functionals; Stokes-Dirac structures; energy variables; infinite-dimensional port-Hamiltonian control systems; interconnection problem; port-Hamiltonian framework; skew-adjoint differential operators; variational derivative; Boundary conditions; Context; Control systems; Couplings; Manifolds; Tensile stress; Vectors; Differential geometry; distributed-parameter systems; port-Hamiltonian systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2012.2235739

Filename

6389716