Related papers: Approximation of the Koopman operator via Bernstei…
While Koopman-based techniques like extended Dynamic Mode Decomposition are nowadays ubiquitous in the data-driven approximation of dynamical systems, quantitative error estimates were only recently established. To this end, both sources of…
Koopman operator theory is a popular candidate for data-driven modeling because it provides a global linearization representation for nonlinear dynamical systems. However, existing Koopman operator-based methods suffer from shortcomings in…
The Koopman operator enables simplified representations for nonlinear systems in data-driven optimal control, but the accompanying uncertainties inevitably induce deviations in the optimal controller and associated value function. This…
Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of…
This paper introduces a data-dependent approximation of the forward kinematics map for certain types of animal motion models. It is assumed that motions are supported on a low-dimensional, unknown configuration manifold $Q$ that is…
A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…
Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function…
For the class of continuous, measure-preserving automorphisms on compact metric spaces, a procedure is proposed for constructing a sequence of finite-dimensional approximations to the associated Koopman operator on a Hilbert space. These…
We propose spectral methods for long-term forecasting of temporal signals stemming from linear and nonlinear quasi-periodic dynamical systems. For linear signals, we introduce an algorithm with similarities to the Fourier transform but…
Koopman operator theory has emerged as a powerful tool for system identification, particularly for approximating nonlinear time-invariant systems (NTIS). This paper considers a network of agents with limited observation capabilities that…
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 paper presents a framework for online learning of the Koopman operator using streaming data. Many complex systems for which data-driven modeling and control are sought provide streaming sensor data, the abundance of which can present…
Koopman-based methods leverage a nonlinear lifting to enable linear regression techniques. Consequently, data generation, learning and prediction is performed through the lens of this lifting, giving rise to a nonlinear manifold that is…
This paper presents a novel identification approach of Koopman models of nonlinear systems with inputs under rather general noise conditions. The method uses deep state-space encoders based on the concept of state reconstructability and an…
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…
In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, Proper Orthogonal Decomposition (POD)…
In this paper we propose a novel approach to compute the Koopman operator from sparse time series data. In recent years there has been considerable interests in operator theoretic methods for data-driven analysis of dynamical systems.…
In quantum computation with continous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to…
Real-world time series are characterized by intrinsic non-stationarity that poses a principal challenge for deep forecasting models. While previous models suffer from complicated series variations induced by changing temporal distribution,…
We analyze the performance of Dynamic Mode Decomposition (DMD)-based approximations of the stochastic Koopman operator for random dynamical systems where either the dynamics or observables are affected by noise. For many DMD algorithms, the…