# Safe Learning-based Observers for Unknown Nonlinear Systems using Bayesian Optimization

arXiv: https://arxiv.org/abs/2005.05888 · HTML: https://mlsanity.com/paper/2005.05888/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 May 2020.

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

- [VABO: Violation-Aware Bayesian Optimization for Closed-Loop Control Performance Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2110.07479/) (2021)
- [Violation-Aware Contextual Bayesian Optimization for Controller Performance Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2301.12099/) (2023)
- [Neural Observer with Lyapunov Stability Guarantee for Uncertain Nonlinear Systems](https://mlsanity.com/paper/2208.13006/) (2022)

## Abstract (arXiv)

Data generated from dynamical systems with unknown dynamics enable the learning of state observers that are: robust to modeling error, computationally tractable to design, and capable of operating with guaranteed performance. In this paper, a modular design methodology is formulated, that consists of three design phases: (i) an initial robust observer design that enables one to learn the dynamics without allowing the state estimation error to diverge (hence, safe); (ii) a learning phase wherein the unmodeled components are estimated using Bayesian optimization and Gaussian processes; and, (iii) a re-design phase that leverages the learned dynamics to improve convergence rate of the state estimation error. The potential of our proposed learning-based observer is demonstrated on a benchmark nonlinear system. Additionally, certificates of guaranteed estimation performance are provided.