SINDy with Control: A Tutorial

TL;DR

This paper reviews data-driven methods, especially SINDy, for identifying nonlinear dynamical models to enable model predictive control of complex systems like infectious diseases.

Contribution

It provides a tutorial on integrating SINDy with MPC, demonstrating its application and comparing it to linear DMD-based MPC for nonlinear system control.

Findings

SINDy-based MPC outperforms linear DMD in nonlinear system control.

The tutorial includes code for practical implementation and extension.

SINDy effectively captures nonlinear dynamics for real-time control.

Abstract

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.