Related papers: Data-driven approximations of dynamical systems op…
In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In…
This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and control of nonlinear dynamics, it is challenging to accurately…
This paper tackles the data-driven approximation of unknown dynamical systems using Koopman-operator methods. Given a dictionary of functions, these methods approximate the projection of the action of the operator on the finite-dimensional…
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…
This paper presents a study of the Koopman operator theory and its application to optimal control of a multi-robot system. The Koopman operator, while operating on a set of observation functions of the state vector of a nonlinear system,…
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…
The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman and von Neumann and was developed in later decades by many…
Nonlinearity in dynamics has long been a major challenge in robotics, often causing significant performance degradation in existing control algorithms. For example, the navigation of bipedal robots can exhibit nonlinear behaviors even under…
In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues,…
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…
Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. The Koopman operator has…
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…
In this article, we present data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media using Koopman operators. Different from the case of autonomous dynamical systems, the Koopman operator family of…
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…
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…
This paper presents the results of identification of vehicle dynamics using the Koopman operator. The basic idea is to transform the state space of a nonlinear system (a car in our case) to a higher-dimensional space, using so-called basis…
A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in…
This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…
Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical systems, facilitating the study of their spectral properties and enabling the prediction of the time evolution of observable quantities. Recent methods…
Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts,…