Results 21 to 30 of about 1,745 (187)
Model-Free Geometric Fault Detection and Isolation for Nonlinear Systems Using Koopman Operator
IEEE Access, 2022 This paper presents a model-free fault detection and isolation (FDI) method for nonlinear dynamical systems using Koopman operator theory and linear geometric technique.
Mohammadhosein Bakhtiaridoust +3 more
doaj +1 more source
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
openaire +1 more source
Sharp Spectral Rates for Koopman Operator Learning [PDF]
, 2023 International audienceNonlinear dynamical systems can be handily described by the associated Koopman operator, whose action evolves every observable of the system forward in time.
Lounici, Karim +3 more
core +5 more sources
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 ...
Corbinian, Schlosser, Milan, Korda
openaire +2 more sources
Measurement + Control, 2022 Omnidirectional mobile manipulators (OMMs) have been widely used due to their high mobility and operating flexibility. However, since OMMs are complex nonlinear systems with uncertainties, the dynamic modeling and control are always challenging problems.
Xuehong Zhu +3 more
doaj +1 more source
Robust Approximation of the Stochastic Koopman Operator
SIAM Journal on Applied Dynamical Systems, 2022 20 pages, six ...
Mathias Wanner, Igor Mezic
openaire +3 more sources
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.
openaire +3 more sources
Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control. [PDF]
PLoS ONE, 2016 In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions.
Steven L Brunton +3 more
doaj +1 more source
A quantitative analysis of Koopman operator methods for system identification and predictions
Comptes Rendus. Mécanique, 2022 We give convergence and cost estimates for a data-driven system identification method: given an unknown dynamical system, the aim is to recover its vector field and its flow from trajectory data.
Zhang, Christophe, Zuazua, Enrique
doaj +1 more source
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
openaire +3 more sources