# Nonlinear System Identification with Prior Knowledge of the Region of Attraction

arXiv: https://arxiv.org/abs/2003.12330 · HTML: https://mlsanity.com/paper/2003.12330/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2020.

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

- [Data-Driven Control with Inherent Lyapunov Stability](https://mlsanity.com/paper/2303.03157/) (2023)
- [Learning of Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2312.09734/) (2023)
- [Learning Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces and Random Features](https://mlsanity.com/paper/2404.07703/) (2024)
- [System Identification via Nuclear Norm Regularization](https://mlsanity.com/paper/2203.16673/) (2022)

## Abstract (arXiv)

We consider the problem of nonlinear system identification when prior knowledge is available on the region of attraction (ROA) of an equilibrium point. We propose an identification method in the form of an optimization problem, minimizing the fitting error and guaranteeing the desired stability property. The problem is approached by joint identification the dynamics and a Lyapunov function verifying the stability property. In this setting, the hypothesis set is a reproducing kernel Hilbert space, and with respect to each point of the given subset of the ROA, the Lie derivative inequality of the Lyapunov function imposes a constraint. The problem is a non-convex infinite-dimensional optimization with infinite number of constraints. To obtain a tractable formulation, only a suitably designed finite subset of the constraints are considered. The resulting problem admits a solution in form of a linear combination of the sections of the kernel and its derivatives. An equivalent optimization problem with a quadratic cost function subject to linear and bilinear constraints is derived. A suitable change of variable gives a convex reformulation of the problem. To reduce the number of hyperparameters, the optimization problem is adapted to the case of diagonal kernels. The method is demonstrate by means of an example.