Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
Milan Korda,Igor Mezic +1 more
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This work extends the Koopman operator to controlled dynamical systems and applies the Extended Dynamic Mode Decomposition (EDMD) to compute a finite-dimensional approximation of the operator in such a way that this approximation has the form of a linearcontrolled dynamical system.About:
This article is published in Automatica.The article was published on 2018-07-01 and is currently open access. It has received 655 citations till now. The article focuses on the topics: Linear dynamical system & Linear system.read more
Citations
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Deep learning for universal linear embeddings of nonlinear dynamics.
TL;DR: It is often advantageous to transform a strongly nonlinear system into a linear one in order to simplify its analysis for prediction and control, so the authors combine dynamical systems with deep learning to identify these hard-to-find transformations.
Book
Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control
Steven L. Brunton,J. Nathan Kutz +1 more
TL;DR: In this paper, the authors bring together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science, and highlight many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy.
Journal ArticleDOI
Deep learning for universal linear embeddings of nonlinear dynamics.
TL;DR: In this paper, the authors leverage deep learning to discover representations of Koopman eigenfunctions from data, and identify nonlinear coordinates on which the dynamics are globally linear using a modified auto-encoder.
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Sparse identification of nonlinear dynamics for model predictive control in the low-data limit.
TL;DR: In this paper, the authors extend the sparse identification of nonlinear dynamics (SINDY) modeling 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.
References
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Survey Constrained model predictive control: Stability and optimality
TL;DR: This review focuses on model predictive control of constrained systems, both linear and nonlinear, and distill from an extensive literature essential principles that ensure stability to present a concise characterization of most of the model predictive controllers that have been proposed in the literature.
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Model predictive control: theory and practice—a survey
TL;DR: The flexible constraint handling capabilities of MPC are shown to be a significant advantage in the context of the overall operating objectives of the process industries and the 1-, 2-, and ∞-norm formulations of the performance objective are discussed.