Data-Driven Robust Output Regulation of Continuous-Time LTI Systems Using Koopman Operators

This article deals with the data-driven robust output regulation for continuous-time linear time-invariant (LTI) systems. Both the system and the signal form of disturbances are unknown. It is assumed that input-output data on a finite-time interval are available for the system in the presence of disturbances. By making use of the Koopman operator theory, the Koopman eigenvalues and modes of the system and the disturbance model are determined by applying the Krylov dynamic mode decomposition to the data. For cyclic LTI systems, it is shown that this Koopman modal analysis is always feasible under generic conditions. With this, a data-driven output feedback regulator is determined on the basis of the internal model principle, which also ensures output regulation in the presence of nondestabilizing model uncertainties. A numerical example demonstrates the results of this article.