SINDy with Control: A Tutorial¶
Authors: Urban Fasel, Eurika Kaiser, J. Nathan Kutz, Bingni W. Brunton, Steven L. Brunton
Published: 2021 (Conference Paper)
Source: IEEE Conference on Decision and Control (CDC)
Algorithm: SINDy with Control
arXiv: 2108.13404
DOI: 10.1109/CDC45484.2021.9683120
Summary¶
Tutorial demonstrating how to extend SINDy to systems with exogenous control inputs (SINDy-C), covering library selection, ensemble methods for robustness, and applications to controlled nonlinear dynamical systems.
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.
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Tags¶
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SINDy
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System identification
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Control
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Nonlinear dynamics
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Data-driven methods