Machine Learning for Sparse Nonlinear Modeling and Control

Machine learning is rapidly advancing nearly every field of science and engineering, and control theory is no exception. In particular, it has shown incredible promise for handling several of the main challenges facing modern dynamics and control, including complexity, unmodeled dynamics, strong nonlinearity, and hidden variables. However, machine learning models are often expensive to train and deploy, fail to generalize beyond the training data, and suffer from a lack of explainability, interpretability, and guarantees, all of which limit their use in real-world and safety-critical control applications. Sparse nonlinear modeling and control techniques are a powerful class of machine learning that promote parsimony through sparse optimization, providing data-efficient models that are more interpretable and generalizable and have proven effective for control. In this review, we explore the use of sparse optimization in the context of machine learning to develop compact models and controllers that are easy to train, require significantly less data, and make low-latency predictions. In particular, we focus on applications in model predictive control and reinforcement learning, two of the foundational algorithms in control theory.