Sparse Identification of Nonlinear Dynamics with Control (SINDYc)

By Steven L. Brunton, Joshua L. Proctor, J. Nathan Kutz. 2016

419 citations recorded by the source corpus.

Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using regression methods, including sparse regression. Specifically, we generalize the sparse identification of nonlinear dynamics (SINDY) algorithm to include external inputs and feedback control. This method is demonstrated on examples including the Lotka-Volterra predator--prey model and the Lorenz system with forcing and control. We also connect the present algorithm with the dynamic mode decomposition (DMD) and Koopman operator theory to provide a broader context.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ec9497045b0b327c5350d65ba999b3608f3de0fa

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In Control and Systems Engineering

In Statistical and Nonlinear Physics

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Citations in the corpus

Multi-scale proper orthogonal decomposition of complex fluid flows (2018, methodology): “An introduction to the Koopman framework is proposed by Brunton et al. (2016a), while extensive reviews on its connection to the DMD are proposed by Mezić (2013), Budǐsić et al. (2012) and Tu et al. (2014).”
Sparse identification of nonlinear dynamics for model predictive control in the low-data limit (2017, methodology): “1 Sparse identification of nonlinear dynamics with control Here, we generalize the sparse identification of nonlinear dynamics (SINDY) method [9] to include inputs and control, building on a previous conference paper [8].”