Output-feedback stabilization of a class of n+m linear hyperbolic ODE-PDE-ODE systems

TL;DR

This paper develops an output-feedback control strategy for stabilizing coupled hyperbolic PDE-ODE systems with boundary interactions, using backstepping and time-delay methods, applicable to actuator-load boundary dynamics.

Contribution

It introduces a novel output-feedback stabilization method for n+m hyperbolic PDE-ODE systems with boundary coupling, combining backstepping and time-delay system techniques.

Findings

Successfully stabilizes boundary-coupled PDE-ODE systems

Designs a state observer using backstepping and delay approaches

Provides a systematic output-feedback control law

Abstract

In this paper, we design an output-feedback controller to stabilize n +m hetero-directional transport partial differential equations (PDEs) coupled on both domain boundaries to ordinary differential equations (ODEs). This class of systems can represent, for instance, actuator and load dynamics at the boundaries of a hyperbolic system. The actuator is located at the connection point between the PDE and one of the ODEs, and we consider anti-collocated PDE measurements. We first design a state-observer by combining the backstepping methodology with time-delay system approaches. We then introduce a state feedback controller using analogous techniques before designing the wanted output-feedback control law.