Output Feedback Stabilization for an Unstable Cascaded ODE-Heat Systems Subject to External Disturbance

In this paper, we are concerned with the output feedback exponential stabilization of cascaded parabolic PDE-ODE system where the control end suffers from the external uncertain disturbance, we design an unknown input type state observer with the disturbance estimator term, which is used to stabilize this cascaded system and compensate the external disturbance simultaneously. The stabilizing state feedback control is designed for the observer system by the three steps backstepping transformations, which is the corresponding observer based output feedback stabilizing control for the original system. Finally, the closed-loop system is shown to be exponentially stable.

1 Introduction

In recent years, the boundary control matched disturbance problem described by partial differential equations(PDEs) has attracted more and more scholar's attention. Hence, there are many different approaches have been applied to copy with these uncertainty disturbance in control system. Such as the most classic backstepping method was used for PDEs in the ideal operational state by [1], has been applied to the stabilization of hyperbolic equation subject to boundary control or observation with harmonic disturbance respectively in [2], internal model principle for output regulation with some special type of disturbance [3], robust boundary control for systems with vessel dynamics for distributed disturbance in [4], and adaptive control for systems with unknown parameters [5], to name just a few, which is an earlier disturbance rejection methods in copying with uncertainty by exploiting estimation/cancellation strategy.