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

arXiv: https://arxiv.org/abs/2605.07052 · HTML: https://mlsanity.com/paper/2605.07052/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 11 of 11)

- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [Interpolating Classifiers Make Few Mistakes](https://mlsanity.com/paper/2101.11815/) (2021)
- [A trajectory-based framework for data-driven system analysis and control](https://mlsanity.com/paper/1903.10723/) (2019)
- [Bridging direct & indirect data-driven control formulations via regularizations and relaxations](https://mlsanity.com/paper/2101.01273/) (2021)
- [Robust and Kernelized Data-Enabled Predictive Control for Nonlinear Systems](https://mlsanity.com/paper/2206.01866/) (2022)
- [Willems' Fundamental Lemma for State-space Systems and its Extension to Multiple Datasets](https://mlsanity.com/paper/2002.01023/) (2020)
- [Willems' Fundamental Lemma for Nonlinear Systems with Koopman Linear Embedding](https://mlsanity.com/paper/2409.16389/) (2024)
- [Data-Driven Internal Model Control of Second-Order Discrete Volterra Systems](https://mlsanity.com/paper/2003.14158/) (2020)
- [The informativity approach to data-driven analysis and control](https://mlsanity.com/paper/2302.10488/) (2023)
- [Data-Based System Analysis and Control of Flat Nonlinear Systems](https://mlsanity.com/paper/2103.02892/) (2021)
- [Exploring the Links between the Fundamental Lemma and Kernel Regression](https://mlsanity.com/paper/2403.05368/) (2024)

## Abstract (arXiv)

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.