Minimum time control of heterodirectional linear coupled hyperbolic PDEs

TL;DR

This paper develops a control method for stabilizing a class of coupled hyperbolic PDEs with opposite directions of transport, achieving minimal time stabilization and observer-based output feedback.

Contribution

It introduces a backstepping approach for minimal time stabilization and output feedback control of heterodirectional linear hyperbolic PDE systems.

Findings

Achieved stabilization in minimal time for the class of PDEs

Developed observer-based output feedback control

Validated the approach through theoretical analysis

Abstract

We solve the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and m leftward convecting transport PDEs. Using the backstepping approach yields solutions to stabilization in minimal time and observer based output feedback.