Kernel-based models for system analysis

TL;DR

This paper presents a kernel-based computational framework for identifying nonlinear input-output operators that fit system trajectories while satisfying integral quadratic constraints, offering an alternative to traditional state-space models.

Contribution

It introduces a novel kernel-based approach for system identification that incorporates system properties directly into the data fitting process, overcoming limitations of state-space models.

Findings

Provides a regularized least squares solution in RKHS for system identification.

Demonstrates the framework's ability to incorporate input-output constraints.

Offers a departure from traditional state-space modeling methods.

Abstract

This paper 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.