| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 29 | |
| Number of page(s) | 30 | |
| DOI | https://doi.org/10.1051/cocv/2025019 | |
| Published online | 31 March 2025 | |
Semi-global stabilization of a nonlinear transport equation with nonlocal velocity
1
Institut de Mathématiques de Bordeaux UMR 5251, Université de Bordeaux and CNRS, 33405 Talence, France
2
School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China
3
School of Mathematical Sciences, Fudan University, Shanghai 200433, China
* Corresponding author: wzq@fudan.edu.cn
Received:
17
March
2024
Accepted:
10
February
2025
In this paper, we establish the semi-global feedback stabilization for a class of nonlinear transport equations with nonlocal velocity, which models a highly re-entrant system encountered in semi-conductor manufacturing. We design two new time-varying feedback laws: one yields a semi-global exponential stability of the corresponding closed-loop system, the other one yields a local exponential stability result for the corresponding closed-loop system. The crucial assumption on the velocity function λ(·) and the target equilibrium ρ̅ is strongly reduced compared to the previous results. Numerical simulations are also provided as illustration of the theoretical results.
Mathematics Subject Classification: 35Q49 / 90B06 / 93C20 / 93D15
Key words: Exponential stabilization / output feedback / time-varying feedback / nonlinear transport equation / nonlocal velocity
© The authors. Published by EDP Sciences, SMAI 2025
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