TY - GEN
T1 - Finite-dimensional homogeneous boundary control for a 1D reaction-diffusion equation
AU - Ayamou, Mericel
AU - Espitia, Nicolas
AU - Polyakov, Andrey
AU - Fridman, Emilia
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024
Y1 - 2024
N2 - In this paper, we address the problem of finite-dimensional boundary stabilization of the 1 D reaction-diffusion equation. Using the modal decomposition approach, we propose a finite-dimensional homogeneous controller, stabilizing the unstable dynamics while ensuring the stability of the residual part. The closed-loop system with homogeneous feedback is well-posed and stable. The proposed controller is proven superior to a finite-dimensional linear feedback controller in terms of closed-loop performance. The numerical simulations are presented to support the analytical results.
AB - In this paper, we address the problem of finite-dimensional boundary stabilization of the 1 D reaction-diffusion equation. Using the modal decomposition approach, we propose a finite-dimensional homogeneous controller, stabilizing the unstable dynamics while ensuring the stability of the residual part. The closed-loop system with homogeneous feedback is well-posed and stable. The proposed controller is proven superior to a finite-dimensional linear feedback controller in terms of closed-loop performance. The numerical simulations are presented to support the analytical results.
UR - http://www.scopus.com/inward/record.url?scp=86000506298&partnerID=8YFLogxK
U2 - 10.1109/CDC56724.2024.10886236
DO - 10.1109/CDC56724.2024.10886236
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AN - SCOPUS:86000506298
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 1962
EP - 1967
BT - 2024 IEEE 63rd Conference on Decision and Control, CDC 2024
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 63rd IEEE Conference on Decision and Control, CDC 2024
Y2 - 16 December 2024 through 19 December 2024
ER -