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Modeling and boundary control of infinite dimensional systems in the Brayton-Moser framework
Published in Oxford University Press
2019
Volume: 36
   
Issue: 2
Pages: 485 - 513
Abstract
It is well documented that shaping the energy of finite-dimensional port-Hamiltonian systems by interconnection is severely restricted due to the presence of dissipation. This phenomenon is usually referred to as the dissipation obstacle. In this paper, we show the existence of dissipation obstacle in infinite dimensional systems. Motivated by this, we present the Brayton-Moser formulation, together with its equivalent Dirac structure. Analogous to finite dimensional systems, identifying the underlying gradient structure is crucial in presenting the stability analysis. We elucidate this through an example of Maxwell's equations with zero energy flows through the boundary. In the case of mixed-finite and infinite-dimensional systems, we find admissible pairs for all the subsystems while preserving the overall structure. We illustrate this using a transmission line system interconnected to finite dimensional systems through its boundary. This ultimately leads to a new passive map, using this we solve a boundary control problem, circumventing the dissipation obstacle. © 2017 The Author(s). Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
About the journal
JournalData powered by TypesetIMA Journal of Mathematical Control and Information
PublisherData powered by TypesetOxford University Press
ISSN02650754
Open AccessNo
Concepts (10)
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    Maxwell equations
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    BOUNDARY CONTROL PROBLEMS
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    BRAYTON-MOSER EQUATIONS
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    FINITE DIMENSIONAL SYSTEMS
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    GRADIENT STRUCTURE
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    INFINITE-DIMENSIONAL SYSTEM
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    MIXED POTENTIAL
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    Port-hamiltonian systems
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    TRANSMISSION LINE SYSTEMS
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    Hamiltonians