ISS-Lyapunov strictification via observer design and integral action control for a Korteweg-de-Vries equation

TL;DR

This paper develops a boundary control strategy for a Korteweg-de-Vries system with disturbances, using an observer-based ISS-Lyapunov functional and forwarding method to achieve output regulation.

Contribution

It introduces a novel ISS-Lyapunov functional for the KdV equation via observer design and integral action control, extending finite-dimensional strictification methods.

Findings

Successfully constructs an ISS-Lyapunov functional for KdV system

Designs an observer using backstepping approach

Achieves output regulation with boundary control

Abstract

The article deals with the output regulation of a Korteweg-de-Vries (KdV) system subject to a distributed disturbance. The control input and the output are located at the boundary. To achieve this objective, we follow a Lyapunov approach. For that, inspired by the strictication methodology proposed in [42] in the finite-dimensional context, we construct an ISS-Lyapunov functional for the KdV equation thanks to the use of an observer designed via the backstepping approach. Then, thanks to this Lyapunov functional, we apply the forwarding method in order to solve the desired output regulation problem.