Sidewise Profile Control of 1-D Waves

Akbulut, Yeşim; Zuazua, Enrique

doi:10.1007/s10957-021-01986-w

Makale Tam Makale Uluslararası 2022

Sidewise Profile Control of 1-D Waves

Yeşim Akbulut, Enrique Zuazua

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS Cilt 193 · Sayı 1-3 · ss. 931–949 · 01.06.2022

DOI ile aç

Özet

We analyze the sidewise controllability for the variable coefficients one-dimensional wave equation. The control is acting on one extreme of the string with the aim that the solution tracks a given path or profile at the other free end. This sidewise profile control problem is also often referred to as nodal profile or tracking control. The problem is reformulated as a dual observability property for the corresponding adjoint system, which is proved by means of sidewise energy propagation arguments in a sufficiently large time, in the class of BV-coefficients. We also present a number of open problems and perspectives for further research.

Anahtar kelimeler

1-D wave equations Sidewise profile controllability Nodal profile control BV-coefficients Sidewise observability Sidewise energy estimates EXACT BOUNDARY CONTROLLABILITY NODAL PROFILE NULL CONTROLLABILITY HEAT-EQUATION OBSERVABILITY NETWORK

Atıf için künye

Akbulut, Y., & Zuazua, E. (2022). Sidewise Profile Control of 1-D Waves. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 193(1-3), 931–949. https://doi.org/10.1007/s10957-021-01986-w

BibTeX

@article{akbulut2022-74525,
  author = {Akbulut, Yeşim and Zuazua, Enrique},
  title = {Sidewise Profile Control of 1-D Waves},
  journal = {JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS},
  year = {2022},
  volume = {193},
  number = {1-3},
  pages = {931--949},
  issn = {0022-3239},
  doi = {10.1007/s10957-021-01986-w},
  url = {https://akademik.atauni.edu.tr/yayinlar/74525-sidewise-profile-control-of-1-d-waves}
}