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

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.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

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