Kernel-Based Models for System Analysis
Henk J. van Waarde, Rodolphe Sepulchre
Abstract
This article introduces a computational framework to identify nonlinear input–output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized by suitable input–output properties required for system analysis and control design. This biased identification problem is shown to admit the tractable solution of a regularized least squares problem when formulated in a suitable reproducing kernel Hilbert space. The kernel-based framework is a departure from the prevailing state-space framework. It is motivated by fundamental limitations of nonlinear state-space models at combining the fitting requirements of data-based modeling with the input–output requirements of system analysis and physical modeling.