Results 11 to 20 of about 780 (160)
Closed-loop Koopman operator approximation
Machine Learning: Science and TechnologyThis paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in terms of an ...
Steven Dahdah, James Richard Forbes
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On the Koopman Operator of Algorithms [PDF]
SIAM Journal on Applied Dynamical Systems, 2020 27 pages, 11 ...
Felix Dietrich +2 more
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Koopman operator for Burgers's equation [PDF]
Physical Review Fluids, 2021 The Koopman decomposition of the Burgers' flow is explicitly derived, the frequencies and the coefficients of this decomposition are identified as eigenvalues and eigenfunctionals of the Koopman operator, and the convergence of the Koopman decomposition is proven for $tg0$ for small Cauchy data, and up to $t=0$ for regular Cauchy data.
Mikhael Balabane +2 more
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Koopman Operators and the $3x+1$-Dynamical System [PDF]
SIAM Journal on Applied Dynamical Systems, 2021 The $3x+1$-problem (or Collatz problem) is a notorious conjecture in arithmetic. It can be viewed as iterating a map and, therefore, it is a dynamical system on the discrete space $\mathbb{N}$ of natural numbers. The emerging dynamical system is studied in the present work with methods from the theory of Koopman operators and $C^*$-algebras.
John Leventides, Costas Poulios
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Symplectic Geometry of the Koopman Operator [PDF]
Doklady Mathematics, 2021 Abstract We consider the Koopman operator generated by an invertible transformation of a space with a finite countably additive measure. If the square of this transformation is ergodic, then the orthogonal Koopman operator is a symplectic transformation on the real Hilbert space of square summable functions with
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Sparsity structures for Koopman operators
IEICE Proceeding Series, 2021 We present a decomposition of the Koopman operator based on the sparse structure of the underlying dynamical system, allowing one to consider the system as a family of subsystems interconnected by a graph. Using the intrinsic properties of the Koopman operator, we show that eigenfunctions for the subsystems induce eigenfunctions for the whole system ...
Schlosser, Corbinian, Korda, Milan
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Renormalization group as a Koopman operator [PDF]
Physical Review E, 2020 Koopman operator theory is shown to be directly related to the renormalization group. This observation allows us, with no assumption of translational invariance, to compute the critical exponents $η$ and $δ$, as well as ratios of critical exponents, of classical spin systems from single observables alone.
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A Koopman Operator Tutorial with Othogonal Polynomials
CoRR, 2021 The Koopman Operator (KO) offers a promising alternative methodology to solve ordinary differential equations analytically. The solution of the dynamical system is analyzed in terms of observables, which are expressed as a linear combination of the eigenfunctions of the system.
Simone Servadio +2 more
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Diffeomorphically Learning Stable Koopman Operators
IEEE Control Systems Letters, 2022 Revised version submitted to IEEE Control Systems Letters (L-CSS) with substantially revised exposition, evaluation and proof of Lemma 2 (previously Lemma 8)
Petar Bevanda +5 more
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Feedback Stabilization Using Koopman Operator [PDF]
2018 IEEE Conference on Decision and Control (CDC), 2018 Accepted for IEEE Conference on Decision and Control(CDC ...
Bowen Huang, Xu Ma 0002, Umesh Vaidya
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