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

E Kaiser1, J N Kutz2, S L Brunton1

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Sparse Identification of Nonlinear Dynamics (SINDY) enhances Model Predictive Control (MPC) for data-driven modeling. SINDY-MPC offers superior performance with less data, improved interpretability, and robustness for real-time applications.

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Area of Science:

  • Control Theory
  • Machine Learning
  • Dynamical Systems

Background:

  • Machine learning, particularly neural networks (NN), offers opportunities for data-driven modeling in control but requires extensive data and lacks interpretability.
  • Existing NN models struggle with online identification, especially after system changes, due to data limitations and generalization issues.

Purpose of the Study:

  • To extend the Sparse Identification of Nonlinear Dynamics (SINDY) method to incorporate system actuation.
  • To demonstrate the effectiveness of SINDY-based Model Predictive Control (SINDY-MPC) for enhancing control performance using limited, noisy data.

Main Methods:

  • Extended the SINDY algorithm to model system dynamics including actuation effects.
  • Developed a SINDY-MPC framework for online model identification and control.
  • Evaluated SINDY-MPC against NN and linear models on diverse dynamical systems.

Main Results:

  • SINDY-MPC models are parsimonious, interpretable, and generalize well.
  • SINDY-MPC significantly outperforms NN models in terms of data efficiency, computational cost, and noise robustness.
  • SINDY-MPC demonstrates superior performance compared to linear data-driven models.

Conclusions:

  • SINDY-MPC provides a viable, data-efficient, and robust approach for online model identification and control, especially in low-data regimes.
  • The framework is effective across various complex systems, including chaotic, flight control, and biomedical models.
  • SINDY-MPC represents a significant advancement for extending model predictive control capabilities.