Energy-based Control of a Wave Equation with Boundary Anti-damping

Authors

A. Macchelli, Y. Le Gorrec, Y. Wu, H. Ramírez

Abstract

In this paper, we consider the asymptotic boundary stabilisation of a one-dimensional wave equation subject to anti-damping at its free end and with control at the opposite one. The control action, implemented through a state feedback or a dynamic controller, is derived by using the port-Hamiltonian framework. More precisely, the standard energy-shaping approach plus damping assignment is adapted to cope with infinite dimensional systems with anti-damping boundary conditions. It is shown how to modify the equivalent dynamic controller to account for the instability propagation along the domain.

Keywords

distributed parameter systems; port-Hamiltonian systems; unstable wave equation; passivity-based control

Citation

• Journal: IFAC-PapersOnLine
• Year: 2020
• Volume: 53
• Issue: 2
• Pages: 7740–7745
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2020.12.1527
• Note: 21st IFAC World Congress- Berlin, Germany, 11–17 July 2020

BibTeX

@article{Macchelli_2020,
  title={{Energy-based Control of a Wave Equation with Boundary Anti-damping}},
  volume={53},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2020.12.1527},
  number={2},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Macchelli, A. and Gorrec, Y. Le and Wu, Y. and Ramírez, H.},
  year={2020},
  pages={7740--7745}
}

Download the bib file

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