Adaptive error feedback regulator design for 1 D heat equation

This paper considers the error feedback regulator problem (EFRP) for 1 D heat equation with general harmonic disturbance and output both anti-collocated with control. We firstly construct an auxiliary system in which the measured error becomes the output. Then an adaptive observer is designed in terms of the measured error to recover the state of the auxiliary system and estimate the unknown parameters. Finally, we construct another auxiliary system in which the control and the anti-collocated disturbance become collocated and thus from which we obtain the adaptive controller design. The control objective which is to regulate the error output to zero and to stabilize exponentially the state of the resulting closed-loop disconnected with disturbance and reference is achieved. (C) 2020 Elsevier Ltd. All rights reserved.