Results 61 to 70 of about 1,063,107 (310)
Data-driven spectral analysis of the Koopman operator
Applied and Computational Harmonic Analysis, 2020 Starting from measured data, we develop a method to compute the fine structure of the spectrum of the Koopman operator with rigorous convergence guarantees. The method is based on the observation that, in the measure-preserving ergodic setting, the moments of the spectral measure associated to a given observable are computable from a single trajectory ...
Mihai Putinar +3 more
openaire +6 more sources
Koopman Operator Spectrum for Random Dynamical Systems [PDF]
Journal of Nonlinear Science, 2019 In this paper we consider the Koopman operator associated with the discrete and the continuous time random dynamical system (RDS). We provide results that characterize the spectrum and the eigenfunctions of the stochastic Koopman operator associated with different types of linear RDS.
Igor Mezic +2 more
openaire +4 more sources
Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians
, 2017 In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to cast a ...
alvin +11 more
core +1 more source
Slow collective variables and molecular kinetics from short off-equilibrium simulations [PDF]
, 2017 Markov state models (MSMs) and master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering.
Klus, Stefan +5 more
core +1 more source
IEEE AccessThis paper proposes Koopman operator-based Stochastic Model Predictive Control (K-SMPC) for enhanced lateral control of autonomous vehicles. The Koopman operator is a linear map representing the nonlinear dynamics in an infinite-dimensional space.
Jin Sung Kim +3 more
doaj +1 more source
Koopman Operators for Modeling and Control of Soft Robotics
Current Robotics Reports, 2023 Abstract Purpose of Review We review recent advances in algorithmic development and validation for modeling and control of soft robots leveraging the Koopman operator theory. Recent Findings We identify the following trends in recent research efforts in this area.
Lu Shi +2 more
openaire +2 more sources
On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator
, 2017 Extended Dynamic Mode Decomposition (EDMD) is an algorithm that approximates the action of the Koopman operator on an $N$-dimensional subspace of the space of observables by sampling at $M$ points in the state space.
Korda, Milan, Mezić, Igor
core +1 more source
Weighted Frobenius-Perron operators and their spectra [PDF]
Mathematica Bohemica, 2017 First, some classic properties of a weighted Frobenius-Perron operator $\mathcal{P}_\varphi^u$ on $L^1(\Sigma)$ as a predual of weighted Koopman operator $W=uU_\varphi$ on $L^\infty(\Sigma)$ will be investigated using the language of the conditional ...
Mohammad Reza Jabbarzadeh +1 more
doaj +1 more source
Koopman Operator-Based Detection-Isolation of Cyberattack: A Case Study on Electric Vehicle Charging [PDF]
American Control ConferenceOne of the key challenges towards the reliable operation of cyber-physical systems (CPS) is the threat of cyberattacks on system actuation signals and measurements.
Sanchita Ghosh, Tanushree Roy
semanticscholar +1 more source
Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator [PDF]
, 2016 In this paper, we further develop a recently proposed control method to switch a bistable system between its steady states using temporal pulses. The motivation for using pulses comes from biomedical and biological applications (e.g.
Goncalves, Jorge +2 more
core +2 more sources