Backstepping Design of Dynamic State Feedback Controllers for Parabolic Systems
Abstract
Recently, dynamic state feedback controllers that are based on dynamic extensions have been presented for heterodirectional hyperbolic systems. In this paper, a similar concept for the control of coupled diffusion-reaction systems is suggested. The introduction of a specific controller dynamics leads to homogenized diffusion coefficients for the extended system. Then, a backstepping-based static state feedback for the dynamically extended system is designed, which, overall, results in a dynamic state feedback. Such a design allows stabilizing a more general class of parabolic systems as well as assigning arbitrary closed-loop dynamics. This can be used, e.g., to achieve a decoupled input-output behavior, which is, in general, not possible with a static state feedback. A simulation example illustrates the results.
Related
- Successive design of backstepping observers for parabolic PDE-ODE systems and its duality to state feedback stabilization
- Input-to-state stability of second-order port-Hamiltonian systems under nonlinear dynamic boundary feedback
- Fredholm Backstepping with Heymann Pre-Feedback for Linearized Navier--Stokes 2D Channel
- Learning Stabilizing Latent Feedback Controllers via Multi-Step Backward Losses
- Parallel Policy-Gradient Methods for Parameter Optimization of Nonlinear Feedback Controllers
BibTeX
@misc{gehring2026backstepping,
title = {{Backstepping Design of Dynamic State Feedback Controllers for Parabolic Systems}},
author = {Nicole Gehring and Benedikt Schwämmle and Abdurrahman Irscheid and Joachim Deutscher},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17293},
eprint = {2609.17293},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17293},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Backstepping Design of Dynamic State Feedback Controllers for Parabolic Systems
AU - Nicole Gehring
AU - Benedikt Schwämmle
AU - Abdurrahman Irscheid
AU - Joachim Deutscher
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17293
UR - https://arxiv.org/abs/2609.17293
AB - Recently, dynamic state feedback controllers that are based on dynamic extensions have been presented for heterodirectional hyperbolic systems. In this paper, a similar concept for the control of coupled diffusion-reaction systems is suggested. The introduction of a specific controller dynamics leads to homogenized diffusion coefficients for the extended system. Then, a backstepping-based static state feedback for the dynamically extended system is designed, which, overall, results in a dynamic state feedback. Such a design allows stabilizing a more general class of parabolic systems as well as assigning arbitrary closed-loop dynamics. This can be used, e.g., to achieve a decoupled input-output behavior, which is, in general, not possible with a static state feedback. A simulation example illustrates the results.
ER -