Time-Varying Internal Models and Regulation of Unknown Harmonic Signals for Regular Linear Systems

Abstract

We introduce general results on well-posedness and output regulation of regular linear systems with nonautonomous controllers. We present a generalization of the internal model principle for time-dependent controllers with asymptotically converging parameters. This general result is utilised in controller design for output tracking and disturbance rejection of harmonic signals with unknown frequencies. Our controller can be flexibly combined with different frequency estimation methods. The results are illustrated in rejection of unknown harmonic disturbances for a one-dimensional boundary controlled heat equation.

arXiv comment34 pages, 2 figures, submitted. The manuscript has been rewritten completely. The previous results were generalised to the class of regular linear systems, and a detailed study of well-posedness of the nonautonomous closed-loop system has been added. The frequency estimation is now completed based on a special auxiliary signal instead of the reference signal