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

Abstract In this paper, we investigate the performance output tracking for a one-dimensional unstable heat equation with input delay and disturbance. Both the performance output and the disturbance are non-collocated to the controller. By writing the time delay as a transport equation, the control plant becomes a cascade system in which the transport equation can be regarded as the actuator dynamics of the unstable heat equation. As a result, the method of actuator dynamics compensation can be used. The difficulties caused by the non-collocated configuration are figured out in the method of trajectory planning. The full state feedback is presented to realize the output tracking, and an error based observer is constructed successfully. The exponential stability of the closed-loop system and the well-posedness of the observer are proved.