# SINDy with Control: A Tutorial

arXiv: https://arxiv.org/abs/2108.13404 · HTML: https://mlsanity.com/paper/2108.13404/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2021.

## Built on by (most cited first, 15 of 15)

- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data](https://mlsanity.com/paper/2305.10706/) (2023)
- [Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data](https://mlsanity.com/paper/2402.15357/) (2024)
- [Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs](https://mlsanity.com/paper/2505.03595/) (2025)
- [Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networks](https://mlsanity.com/paper/2501.11350/) (2025)
- [LES-SINDy: Laplace-Enhanced Sparse Identification of Nonlinear Dynamical Systems](https://mlsanity.com/paper/2411.01719/) (2024)
- [Interpretable and Efficient Data-driven Discovery and Control of Distributed Systems](https://mlsanity.com/paper/2411.04098/) (2024)
- [A Symbolic Representation of Human Posture for Interpretable Learning and Reasoning](https://mlsanity.com/paper/2210.08998/) (2022)
- [SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study](https://mlsanity.com/paper/2403.00578/) (2024)
- [Identifying Unknown Stochastic Dynamics via Finite expression methods](https://mlsanity.com/paper/2504.07085/) (2025)
- [Optimizing Hard Thresholding for Sparse Model Discovery](https://mlsanity.com/paper/2504.20256/) (2025)
- [Data-Driven Discovery and Formulation Refines the Quasi-Steady Model of Flapping-Wing Aerodynamics](https://mlsanity.com/paper/2508.18703/) (2025)
- [Zero-Shot Function Encoder-Based Differentiable Predictive Control](https://mlsanity.com/paper/2511.05757/) (2025)
- [Sparse Kalman Identification for Partially Observable Systems via Adaptive Bayesian Learning](https://mlsanity.com/paper/2511.18051/) (2025)
- [From STLS to Projection-based Dictionary Selection in Sparse Regression for System Identification](https://mlsanity.com/paper/2512.14404/) (2025)

## Abstract (arXiv)

Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based optimization technique that enables the control of such nonlinear systems with constraints. However, modern systems often lack computationally tractable models, motivating the use of system identification techniques to learn accurate and efficient models for real-time control. In this tutorial article, we review emerging data-driven methods for model discovery and how they are used for nonlinear MPC. In particular, we focus on the sparse identification of nonlinear dynamics (SINDy) algorithm and show how it may be used with MPC on an infectious disease control example. We compare the performance against MPC based on a linear dynamic mode decomposition (DMD) model. Code is provided to run the tutorial examples and may be modified to extend this data-driven control framework to arbitrary nonlinear systems.