Output-Feedback Stabilization of the Korteweg-de Vries Equation
Agus Hasan
TL;DR
This paper develops a boundary output-feedback control strategy for stabilizing the Korteweg-de Vries equation with sensors and actuators at different boundaries, using backstepping and Lyapunov methods, validated by numerical simulations.
Contribution
It introduces a novel boundary output-feedback stabilization approach for the KdV equation with anti-collocated sensors and actuators using backstepping.
Findings
Successful stabilization of the KdV equation demonstrated
Backstepping-based control law derived and validated
Numerical simulations confirm theoretical results
Abstract
The present paper develops boundary output-feedback stabilization of the Korteweg-de Vries (KdV) equation with sensors and an actuator located at different boundaries (anti collocated set-up) using backstepping method. The feedback control law and output injection gains are found using the backstepping method for linear KdV equation. The proof of stability is based on construction of a strict Lyapunov functional which includes the observer states. A numerical simulation is presented to validate the result.
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