Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based optimization technique that enables the control of such nonlinear systems with constraints. However, modern systems often lack computationally tractable models, motivating the use of system identification techniques to learn accurate and efficient models for real-time control. In this project, we review emerging data-driven methods for model discovery and how they are used for nonlinear MPC. In particular, we focus on the sparse identification of nonlinear dynamics (SINDy) algorithm and show how it may be used with MPC on an infectious disease control example. We compare the performance against MPC based on a linear dynamic mode decomposition (DMD) model. We provide a tutorial with code to run examples that may be modified to extend this data-driven control framework to arbitrary nonlinear systems.
Nicola Fonzi, Steven L. Brunton, Urban Fasel
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 476(2239), 2020 Jun 28