Related papers: Koopman for stochastic dynamics: error bounds for …
In this paper, we provide a tutorial overview and an extension of a recently developed framework for data-driven control of unknown nonlinear systems with rigorous closed-loop guarantees. The proposed approach relies on the Koopman operator…
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…
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…
We find probability error bounds for approximations of functions $f$ in a separable reproducing kernel Hilbert space $\mathcal{H}$ with reproducing kernel $K$ on a base space $X$, firstly in terms of finite linear combinations of functions…
Transfer operators such as Perron-Frobenius or Koopman operator play a key role in modeling and analysis of complex dynamical systems, which allow linear representations of nonlinear dynamics by transforming the original state variables to…
This paper introduces a new theoretical and computational framework for a data driven Koopman mode analysis of nonlinear dynamics. To alleviate the potential problem of ill-conditioned eigenvectors in the existing implementations of the…
A new dynamic mode decomposition (DMD) method is introduced for simultaneous online system identification and denoising in conjunction with the adoption of an extended Kalman filter algorithm\color{black}. The present paper explains the…
We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. We cast the Dynamic Mode-Decomposition type…
The global behavior of dynamical systems can be studied by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with the system. Two important operators which are frequently used to gain insight into the…
Transfer operators such as the Perron--Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operators can be used to detect metastable sets, to project the…
This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size bounds on the approximation error are established for posterior…
This paper presents a new technique for norm-convergent dynamic mode decomposition of deterministic systems. The developed method utilizes recent results on singular dynamic mode decomposition where it is shown that by appropriate selection…
We consider policy evaluation in infinite-horizon discounted Markov decision problems (MDPs) with infinite spaces. We reformulate this task a compositional stochastic program with a function-valued decision variable that belongs to a…
This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…
We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a vector-valued reproducing kernel Hilbert space induced by an…
We introduce a novel conditional density estimation model termed the conditional density operator (CDO). It naturally captures multivariate, multimodal output densities and shows performance that is competitive with recent neural…
Understanding and modeling complex dynamic systems is crucial for enhancing vehicle performance and safety, especially in the context of autonomous driving. Recently, popular methods such as Koopman operators and their approximators, known…
The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework naturally yields linear embedding models, there have been…
System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…
We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the…