# Specialized Interior Point Algorithm for Stable Nonlinear System Identification

arXiv: https://arxiv.org/abs/1803.01066 · HTML: https://mlsanity.com/paper/1803.01066/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2018.

## Built on by (most cited first, 3 of 3)

- [Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness](https://mlsanity.com/paper/2104.05942/) (2021)
- [React to Surprises: Stable-by-Design Neural Feedback Control and the Youla-REN](https://mlsanity.com/paper/2506.01226/) (2025)
- [Distributed Identification of Contracting and/or Monotone Network Dynamics](https://mlsanity.com/paper/2107.14309/) (2021)

## Abstract (arXiv)

Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming (SDP), however the resulting SDPs have large dimension, limiting their utility in practical problems. In this paper we develop a path-following interior point algorithm that takes advantage of special structure in the problem and reduces computational complexity from cubic to linear growth with the length of the data set. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, and we demonstrate superior generalization to new data. We also explore the "regularizing" effect of stability constraints as an alternative to regressor subset selection.