Output Feedback Stabilization of Semilinear Parabolic PDEs using\n Backstepping

2016/12/12 by Agus Hasan, Hasan, Agus
Computer Science · Engineering · 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

paper · pdf · doi:10.48550/arxiv.1612.03867

openalex publication_date 2016/12/12 · 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\nof semilinear parabolic PDEs with a boundary measurement and an actuation\nlocated at the same place. The method uses backstepping transformations, where\nthe state and error systems are proved to be locally exponentially stable in\nthe \ℍ⁴ norm. The stability of the transformed systems are obtained\nby constructing a strict Lyapunov function. A numerical example using the\nFitzHugh-Nagumo equation shows the proposed control law stabilizes the system\ninto its equilibrium solution.\n

Citations

• Impulses and Physiological States in Theoretical Models of Nerve Membrane

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