Active disturbance rejection control approach to the output tracking of PDEs with general disturbances: A new perspective

Abstract

In recent years, significant progress has been made in output regulation for systems described by partial differential equations (PDEs) through the active disturbance rejection control approach (ADRC). However, in all these studies, the disturbance typically manifests in a single channel and requires estimation, often necessitating additional measured signals. This is because the disturbance must be identified through the output. In this paper, we approach this problem from a novel perspective: disturbances occur in all channels, yet few measured signals are required. In most cases, only the tracking error is utilized as the measured signal. This marks a significant advancement in the application of ADRC to PDEs. We primarily demonstrate this approach by addressing the output tracking problem for a multi-dimensional heat equation, considering general disturbances across all possible channels. Additionally, we briefly discuss some other one-dimensional problems studied in the literature, such as the one-dimensional wave equation.