A data-driven immersion technique for linearization of discrete-time nonlinear systems

Abstract

This paper proposes a data-driven immersion approach to obtain linear equivalents or approximations of discrete-time nonlinear systems. Exact linearization can only be achieved for very particular classes of systems. In general cases, we aim to obtain a finite-time linear approximation. Our approach only takes a finite set of trajectories and hence an analytic model is not required. The mismatch between the approximate linear model and the original system is concretely discussed with formal bounds. We also provide a Koopman-operator interpretation of this technique, which shows a link between system immersibility and the Koopman operator theory. Several numerical examples are taken to show the capabilities of the proposed immersion approach. Comparison is also made with other Koopman-based lifting approaches which use radial basis functions and monomials.