# Kernel-based models for system analysis

arXiv: https://arxiv.org/abs/2110.11735 · HTML: https://mlsanity.com/paper/2110.11735/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2021.

## Built on by (most cited first, 4 of 4)

- [Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context](https://mlsanity.com/paper/2503.20341/) (2025)
- [Learning Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces and Random Features](https://mlsanity.com/paper/2404.07703/) (2024)
- [Fading memory and the convolution theorem](https://mlsanity.com/paper/2408.07386/) (2024)
- [Lipschitz bounds for integral kernels](https://mlsanity.com/paper/2604.02887/) (2026)

## Abstract (arXiv)

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.