Performance output tracking for a one-dimensional heat equation with input delay

Abstract

In this paper, we focus on the performance output tracking for a one-dimensional heat partial differential equation with unknown external disturbance and non-collocated configuration, in which the control input is subject to a time delay. By writing the time delay as a first-order hyperbolic equation, the control system can be modeled as a cascade construction in which the transport equation can be viewed as the actuator dynamics of the heat partial differential system. With the help of the actuator dynamics compensation, the difficulties caused by input delay are addressed. The full state feedback law is constructed to achieve the performance output tracking and an error based observer is designed successfully. The exponential stability of the closed-loop system and the well-posedness of the observer are obtained.