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

By Eurika Kaiser, J. Nathan Kutz, Steven L. Brunton. Proceedings of the Royal Society A, 2017

681 citations recorded by the source corpus.

Data-driven discovery of dynamics via machine learning is pushing the frontiers of modelling and control efforts, providing a tremendous opportunity to extend the reach of model predictive control (MPC). However, many leading methods in machine learning, such as neural networks (NN), 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. These factors limit their use for the online identification of a model in the low-data limit, for example following an abrupt change to the system dynamics. In this work, we extend the recent sparse identification of nonlinear dynamics (SINDY) modelling procedure to include the effects of actuation and demonstrate the ability of these models to enhance the performance of 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. We show that the resulting SINDY-MPC framework has higher performance, requires significantly less data, and is more computationally efficient and robust to noise than NN models, 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. SINDY-MPC is demonstrated on a variety of dynamical systems with different challenges, including the chaotic Lorenz system, a simple model for flight control of an F8 aircraft, and an HIV model incorporating drug treatment.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b2eb064f432557c59ce99834d7dc7817e4687271

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Citations in the corpus

Bridging Direct and Indirect Data-Driven Control Formulations via Regularizations and Relaxations (2021, background): “Consider the discrete-time nonlinear Lotka-Volterra dynamics considered for direct data-driven control in [57]”
Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control (2021, methodology): “The control problem is based on Kaiser et al. [43], where the MPC cost function and weight matrices are described in detail.”
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics (2020, methodology): “In a short time, the SINDy algorithm has been extended to include inputs and control [47], to identify partial differential equations [29, 32], to incorporate physically relevant constraints [34], to include tensor bases [44], and to incorporate integral terms for denoising [48, 49].”
Data-driven discovery of coordinates and governing equations (2019, methodology): “SINDy has been widely applied to identify models for ﬂuid ﬂows [40, 51], optical systems [52], chemical reaction dynamics [53], convection in a plasma [54], structural modeling [55], and for model predictive control [56].”
Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, neutral): “Discover Governing Equations [30] [227] [37] [167] [168] [216] [123] [200][205] [52] [141] [290] [207] [155] [251]”