Modeling and boundary control of infinite dimensional systems in the Brayton–Moser framework

Authors

Krishna Chaitanya Kosaraju, Ramkrishna Pasumarthy, Dimitri Jeltsema

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.

Citation

• Journal: IMA Journal of Mathematical Control and Information
• Year: 2019
• Volume: 36
• Issue: 2
• Pages: 485–513
• Publisher: Oxford University Press (OUP)
• DOI: 10.1093/imamci/dnx057

BibTeX

@article{Chaitanya_Kosaraju_2017,
  title={{Modeling and boundary control of infinite dimensional systems in the Brayton–Moser framework}},
  volume={36},
  ISSN={1471-6887},
  DOI={10.1093/imamci/dnx057},
  number={2},
  journal={IMA Journal of Mathematical Control and Information},
  publisher={Oxford University Press (OUP)},
  author={Chaitanya Kosaraju, Krishna and Pasumarthy, Ramkrishna and Jeltsema, Dimitri},
  year={2017},
  pages={485--513}
}

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