Output-Feedback Stabilization of the Korteweg-de Vries Equation

The present paper develops boundary output-feedback stabilization of the Korteweg-de Vries (KdV) equation with sensors and actuators are located at different boundaries (anti collocated set-up) using backstepping method. The feedback control law and the output injection gains are developed from the backstepping method for the linear KdV equation. The novelty of this paper is the nonlinear observer for the KdV equation. Furthermore, 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.