Dirac structures and boundary control systems associated with skew-symmetric differential operators

Associated with a skew-symmetric linear operator on the spatial domain $[a,b]$ we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac structure is a subspace of a Hilbert space. Naturally, associated with this Dirac structure is an infinite-d...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2005-01, Vol.44 (5), p.1864-1892
Main Authors: LE GORREC, Y, ZWART, H, MASCHKE, B
Format: Article
Language:English
Subjects:
Applied mathematics
Applied sciences
Codes
Computer science
control theory
systems
Control theory. Systems
Exact sciences and technology
Hilbert space
Mathematical programming
Miscellaneous
Modelling and identification
Operational research and scientific management
Operational research. Management science
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Summary:Associated with a skew-symmetric linear operator on the spatial domain $[a,b]$ we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac structure is a subspace of a Hilbert space. Naturally, associated with this Dirac structure is an infinite-dimensional system. We parameterize the boundary port variables for which the \( C_{0} \)-semigroup associated with this system is contractive or unitary. Furthermore, this parameterization is used to split the boundary port variables into inputs and outputs. Similarly, we define a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and a symmetric positive operator defining the energy of the system. We illustrate this theory on the example of the Timoshenko beam.
ISSN:0363-0129
1095-7138
DOI:10.1137/040611677