# A Physics-informed Machine Learning-based Control Method for Nonlinear Dynamic Systems with Highly Noisy Measurements

arXiv: https://arxiv.org/abs/2311.07613 · HTML: https://mlsanity.com/paper/2311.07613/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 12 Nov 2023.

## Builds on (most cited first, 5 of 5)

- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization](https://mlsanity.com/paper/2206.00176/) (2022)
- [Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systems](https://mlsanity.com/paper/2011.03699/) (2020)
- [Compressive-sensing-assisted mixed integer optimization for dynamical system discovery with highly noisy data](https://mlsanity.com/paper/2209.12663/) (2022)
- [Gaussian Process (GP)-based Learning Control of Selective Laser Melting Process](https://mlsanity.com/paper/2010.04712/) (2020)

## Built on by (most cited first, 1 of 1)

- [AFSD-Physics: Exploring the governing equations of temperature evolution during additive friction stir deposition by a human-AI teaming approach](https://mlsanity.com/paper/2401.16501/) (2024)

## Abstract (arXiv)

This study presents a physics-informed machine learning-based control method for nonlinear dynamic systems with highly noisy measurements. Existing data-driven control methods that use machine learning for system identification cannot effectively cope with highly noisy measurements, resulting in unstable control performance. To address this challenge, the present study extends current physics-informed machine learning capabilities for modeling nonlinear dynamics with control and integrates them into a model predictive control framework. To demonstrate the capability of the proposed method we test and validate with two noisy nonlinear dynamic systems: the chaotic Lorenz 3 system, and turning machine tool. Analysis of the results illustrate that the proposed method outperforms state-of-the-art benchmarks as measured by both modeling accuracy and control performance for nonlinear dynamic systems under high-noise conditions.