  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.
