Identification of contractive Lur'e-type systems via kernel-based Lipschitz design

TL;DR

This paper introduces a kernel-based method for identifying contractive Lur'e-type systems, combining prior knowledge with Lipschitz design to produce accurate, interpretable, and physically meaningful models.

Contribution

It presents a novel identification framework that enforces contractivity through Lipschitz constant design within a kernel representation, improving model accuracy and interpretability.

Findings

Enforcing contractivity improves parameter estimation.

Models are accurate and physically meaningful.

The approach integrates prior knowledge with kernel methods.

Abstract

This paper addresses the problem of identifying contractive Lur'e-type systems. Specifically, it proposes an identification framework that integrates linear prior knowledge with a kernel representation of the nonlinear feedback while systematically enforcing contractivity via Lipschitz constant design. The resulting algorithms provide models that are accurate in prediction, interpretable, and faithful to the contractive nature of the true system. Numerical experiments demonstrate that enforcing contractivity significantly improves parameter estimation and yields models that are both accurate and physically meaningful.