Output Feedback Stabilization of Semilinear Parabolic PDEs using Backstepping

2016/12/12 by Agus Hasan, Hasan, Agus
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Model Reduction and Neural Networks #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1612.03867

arxiv created 2016/12/12 · openalex publication_date 2016/12/12 · arxiv updated 2016/12/13 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we present output feedback boundary stabilization for a class of semilinear parabolic PDEs with a boundary measurement and an actuation located at the same place. The method uses backstepping transformations, where the state and error systems are proved to be locally exponentially stable in the ℍ⁴ norm. The stability of the transformed systems are obtained by constructing a strict Lyapunov function. A numerical example using the FitzHugh-Nagumo equation shows the proposed control law stabilizes the system into its equilibrium solution.

Citations

• Impulses and Physiological States in Theoretical Models of Nerve Membrane

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