Output-based receding horizon stabilizing control

TL;DR

This paper develops an output-based receding horizon control method combined with a Luenberger observer to stabilize parabolic equations using localized actuators and sensors, with theoretical guarantees and numerical validation.

Contribution

It introduces a novel output-based receding horizon control framework for parabolic equations with localized sensors and actuators, providing stability guarantees.

Findings

Stabilization of parabolic equations using localized actuators and sensors.

Theoretical guarantees for the stabilizing control input.

Numerical simulations validating the control approach.

Abstract

A receding horizon control framework is coupled with a Luenberger observer to construct an output-based control input stabilizing parabolic equations. The actuators and sensors are indicator functions of small subdomains, representing localized actuation and localized measurements. It is shown that, for a class of explicitly given sets of actuators and sensors, we can guarantee the stabilizing property of the constructed input. Results of numerical simulations are presented validating the theoretical findings.