Related papers: Consistent spectral approximation of Koopman opera…
Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite 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 Koopman operator framework holds promise for spectral analysis of nonlinear dynamical systems based on linear operators. Eigenvalues and eigenfunctions of the Koopman operator, so-called Koopman eigenvalues and Koopman eigenfunctions,…
Kernel transfer operators, which can be regarded as approximations of transfer operators such as the Perron-Frobenius or Koopman operator in reproducing kernel Hilbert spaces, are defined in terms of covariance and cross-covariance…
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…
The motivation of our research is to establish a Laplace-domain theory that provides principles and methodology to analyze and synthesize systems with nonlinear dynamics. A semigroup of composition operators defined for nonlinear autonomous…
Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness…
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. Assuming that the…
A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\'e's geometric picture that focuses on "dynamics of states". While this picture has fueled our field for a century, it has shown…
Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…
The Koopman and Perron Frobenius transport operators are fundamentally changing how we approach dynamical systems, providing linear representations for even strongly nonlinear dynamics. Although there is tremendous potential benefit of such…
We develop a framework for dimension reduction, mode decomposition, and nonparametric forecasting of data generated by ergodic dynamical systems. This framework is based on a representation of the Koopman and Perron-Frobenius groups of…
This paper presents a novel approach for estimating the Koopman operator defined on a reproducing kernel Hilbert space (RKHS) and its spectra. We propose an estimation method, what we call Jet Extended Dynamic Mode Decomposition (JetEDMD),…
The Koopman operator presents an attractive approach to achieve global linearization of nonlinear systems, making it a valuable method for simplifying the understanding of complex dynamics. While data-driven methodologies have exhibited…
In this paper, we study how the Koopman operator framework can be combined with kernel methods to effectively control nonlinear dynamical systems. While kernel methods have typically large computational requirements, we show how random…
Optimal sensor placement is an important yet unsolved problem in control theory. In biological organisms, genetic activity is often highly nonlinear, making it difficult to design libraries of promoters to act as reporters of the cell…
Koopman operators are of infinite dimension and capture the characteristics of nonlinear dynamics in a lifted global linear manner. The finite data-driven approximation of Koopman operators results in a class of linear predictors, useful…
The control of legged robots, particularly humanoid and quadruped robots, presents significant challenges due to their high-dimensional and nonlinear dynamics. While linear systems can be effectively controlled using methods like Model…
The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspired formulation of classical mechanics. The main advantage…
Representing nonlinear dynamical systems using the Koopman Operator and its spectrum has distinct advantages in terms of linear interpretability of the model as well as in analysis and control synthesis through the use of well-studied…