Predictor-Based Stabilization of a Delayed Hetero-Dimensional Shoreline--Bathymetry System
Abstract
Exponential stabilization is investigated for a hetero-dimensional parabolic system in which a one-dimensional shoreline subsystem, subject to a constant input delay, is bidirectionally coupled with unactuated two-dimensional bathymetric dynamics. A spectral decomposition separates the finite-dimensional critical shoreline modes from the exponentially stable residual dynamics. State feedback is designed on the critical subspace and lifted to the full shoreline space. An auxiliary transport equation represents the delay, while a predictor removes the explicit input delay from the nominal predictor dynamics. Exponential stability of the full coupled system is established by combining shoreline stabilization and bathymetric coercivity using weighted input--output estimates and a small-gain condition on the hetero-dimensional interaction. Numerical simulations show that uncompensated delayed feedback can strongly amplify both shoreline and bathymetric responses, whereas predictor compensation restores decay of the critical shoreline dynamics and prevents delay-induced amplification from propagating to the unactuated bathymetric subsystem.
Related
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BibTeX
@misc{cisse2026predictorbased,
title = {{Predictor-Based Stabilization of a Delayed Hetero-Dimensional Shoreline--Bathymetry System}},
author = {Amadou Cissé and Mohamed Boutayeb},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34938},
eprint = {2609.34938},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34938},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Predictor-Based Stabilization of a Delayed Hetero-Dimensional Shoreline--Bathymetry System
AU - Amadou Cissé
AU - Mohamed Boutayeb
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34938
UR - https://arxiv.org/abs/2609.34938
AB - Exponential stabilization is investigated for a hetero-dimensional parabolic system in which a one-dimensional shoreline subsystem, subject to a constant input delay, is bidirectionally coupled with unactuated two-dimensional bathymetric dynamics. A spectral decomposition separates the finite-dimensional critical shoreline modes from the exponentially stable residual dynamics. State feedback is designed on the critical subspace and lifted to the full shoreline space. An auxiliary transport equation represents the delay, while a predictor removes the explicit input delay from the nominal predictor dynamics. Exponential stability of the full coupled system is established by combining shoreline stabilization and bathymetric coercivity using weighted input--output estimates and a small-gain condition on the hetero-dimensional interaction. Numerical simulations show that uncompensated delayed feedback can strongly amplify both shoreline and bathymetric responses, whereas predictor compensation restores decay of the critical shoreline dynamics and prevents delay-induced amplification from propagating to the unactuated bathymetric subsystem.
ER -