Sparse identification of nonlinear dynamics for model predictive control in the low-data limit

This work extends the recent sparse identification of nonlinear dynamics (SINDY) modeling procedure to include the effects of actuation and demonstrate the ability of these models to enhance the performance of model predictive control (MPC), based on limited, noisy data. SINDY models are parsimonious, identifying the fewest terms in the model needed to explain the data, making them interpretable and generalizable. Many leading methods in machine learning, such as neural networks, require large volumes of training data, may not be interpretable, do not easily include known constraints and symmetries, and may not generalize beyond the attractor where models are trained. In contrast, we demonstrate that the resulting SINDY-MPC framework has higher performance, requires significantly less data, and is more computationally efficient and robust to noise, making it viable for online training and execution in response to rapid system changes. SINDY-MPC also shows improved performance over linear data driven models, although linear models may provide a stopgap until enough data is available for SINDY.