Energy-shaping and entropy-assignment boundary control of the heat equation

Authors

Luis A. Mora, Yann Le Gorrec, Hector Ramirez

Abstract

This paper shows a finite-dimensional controller design for the boundary control of the heat equation on a 1D spatial domain. The controller exponentially stabilizes the plant at the desired equilibrium profile. The controller is defined using irreversible port-Hamiltonian systems formulation, and it is motivated by passivity-based control techniques developed for port-Hamiltonian systems defined on 1D spatial domains. The boundary controller is designed to have an exponentially stabilizing energy-shaping and entropy-assignment effect. It works with an actuation at one boundary and a reflective boundary condition at the other. The controller can handle situations where measurements are available at only one or both boundaries. The paper characterizes the existence of structural invariant functions to shape the closed-loop energy and assign the required closed-loop entropy. The design approach is illustrated through numerical simulations.

Keywords

Irreversible port-Hamiltonian systems; Heat equation; Boundary control; Passivity-based control

Citation

Journal: Systems & Control Letters
Year: 2024
Volume: 189
Issue:
Pages: 105821
Publisher: Elsevier BV
DOI: 10.1016/j.sysconle.2024.105821

BibTeX

@article{Mora_2024,
  title={{Energy-shaping and entropy-assignment boundary control of the heat equation}},
  volume={189},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2024.105821},
  journal={Systems &amp; Control Letters},
  publisher={Elsevier BV},
  author={Mora, Luis A. and Le Gorrec, Yann and Ramirez, Hector},
  year={2024},
  pages={105821}
}

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