# Contracting Nonlinear Observers: Convex Optimization and Learning from Data

arXiv: https://arxiv.org/abs/1711.08135 · HTML: https://mlsanity.com/paper/1711.08135/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2017.

## 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)
- [Unconstrained Parametrization of Dissipative and Contracting Neural Ordinary Differential Equations](https://mlsanity.com/paper/2304.02976/) (2023)
- [Controller Design for Structured State-space Models via Contraction Theory](https://mlsanity.com/paper/2604.07069/) (2026)

## Abstract (arXiv)

A new approach to design of nonlinear observers (state estimators) is proposed. The main idea is to (i) construct a convex set of dynamical systems which are contracting observers for a particular system, and (ii) optimize over this set for one which minimizes a bound on state-estimation error on a simulated noisy data set. We construct convex sets of continuous-time and discrete-time observers, as well as contracting sampled-data observers for continuous-time systems. Convex bounds for learning are constructed using Lagrangian relaxation. The utility of the proposed methods are verified using numerical simulation.