A Behavioral Framework for Data-Driven Modeling of Nonlinear Systems in Vector-Valued Reproducing Kernel Hilbert Spaces

2026-05-07

AI Summary

This work proposes a data-driven modeling approach for a broad class of nonlinear systems encompassing Volterra series, autoregressive models, and Hammerstein-type state-space realizations, without requiring explicit system identification. By extending Willems’ behavioral theory to vector-valued reproducing kernel Hilbert spaces (RKHS) and integrating minimal-norm interpolation with subspace identification techniques, the authors establish a unified framework for nonlinear system modeling. This study presents the first formulation of behavioral systems theory in vector-valued RKHS, thereby circumventing conventional identification procedures. The resulting framework enables direct application to simulation and control tasks and is applicable to a wide range of nonlinear dynamical systems.

Abstract

We generalize Jan Willems' behavioral approach to a class of discrete-time nonlinear systems in a vector-valued reproducing kernel Hilbert space (RKHS). Apart from linear time-invariant systems, this class covers nonlinear systems modeled by Volterra series and their autoregressive variants, as well as systems admitting Hammerstein-type state-space realizations. We apply the proposed framework to the problem of data-driven modeling of such systems, i.e., when simulation or control objectives for an unknown system are carried out without an explicit system identification step. To that end, we link the behavioral approach to two data-driven modeling methods in a vector-valued RKHS: (1) minimum-norm interpolation and (2) subspace identification.

Problem

• nonlinear systems
• data-driven modeling
• behavioral approach
• vector-valued RKHS
• system identification

Innovation

• behavioral approach
• vector-valued RKHS
• data-driven modeling
• nonlinear systems
• subspace identification