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Nonparametric Control Koopman Operators
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This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental equivalences between different model representations, we are able to close the gap of control system operator learning and infinite-dimensional regression, enabling various empirical estimators and the connection to the well-understood learning theory in RKHSs under one unified framework. Consequently, our proposed framework allows for arbitrarily accurate finite-rank approximations in infinite-dimensional spaces and leads to finite-dimensional predictors without a priori restrictions to a finite span of functions or inputs. To enable applications to high-dimensional control systems, we improve the scalability of our proposed control Koopman operator estimates by utilizing sketching techniques. Numerical experiments demonstrate superior prediction accuracy compared to bilinear EDMD, especially in high dimensions. Finally, we show that our learned models are readily interfaced with linear-parameter-varying techniques for model predictive control.
Forward citations
Cited by 5 Pith papers
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Exact Finite Koopman Embedding of Block-Oriented Polynomial Systems
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A kernel regression of the controlled diffusion generator is combined with a convex HJB recursion to produce data-driven, approximately globally optimal feedback policies.
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Data-Driven Domain of Attraction Estimation via Convergent Koopman-Zubov Approximation
A new RKHS construction gives the Zubov-Koopman operator a spectrum inside the unit disk, so the Zubov function can be estimated from data with a sectorially bounded error.
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Koopman Operator for Stability Analysis: Theory with a Linear--Radial Product Reproducing Kernel
A product of linear and Wendland kernels is proposed so that the Koopman operator's spectrum lies in the unit disk exactly when a conjugate linear system is stable.
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