Sparse Identification of Nonlinear Dynamics with Control (SINDYc)

TL;DR

This paper extends the SINDY algorithm to identify nonlinear dynamical systems with inputs and control, demonstrating its effectiveness on biological and chaotic models, and connecting it with DMD and Koopman theory.

Contribution

It introduces a generalized SINDYc algorithm for systems with control inputs, expanding the applicability of sparse identification methods.

Findings

Successfully identified models for predator-prey and Lorenz systems with control.

Established connections between SINDYc, DMD, and Koopman operator theory.

Demonstrated the method's ability to handle systems with external forcing and feedback control.

Abstract

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.