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.
GitHub: https://github.com/urban-fasel/SEIR_SINDY_MPC
GitHub: https://github.com/urban-fasel/SEIR_SINDY_MPC
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Schematic of the data-driven MPC framework. Using either linear DMD, sparse nonlinear SINDy, or neural network models for predictive control.