Related papers: Asymptotically Stable Data-Driven Koopman Operator…

We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables.…

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…

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…

In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…

The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most…

The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…

Stabilization, disturbance rejection, and control of optical beams and optical spots are ubiquitous problems that are crucial for the development of optical systems for ground and space telescopes, free-space optical communication…

Advances in machine learning and the growing trend towards effortless data generation in real-world systems has led to an increasing interest for data-inferred models and data-based control in robotics. It seems appealing to govern robots…

Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…

Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering…

In the computational sciences, one must often estimate model parameters from data subject to noise and uncertainty, leading to inaccurate results. In order to improve the accuracy of models with noisy parameters, we consider the problem of…

Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…

Data-driven neural Koopman operator theory has emerged as a powerful tool for linearizing and controlling nonlinear robotic systems. However, the performance of these data-driven models fundamentally depends on the trade-off between sample…

It is hard to identify nonlinear biological models strictly from data, with results that are often sensitive to experimental conditions. Automated experimental workflows and liquid handling enables unprecedented throughput, as well as the…

Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…

In this paper, we propose a novel controller design approach for unknown nonlinear systems using the Koopman operator. In particular, we use the recently proposed stability- and feedback-oriented extended dynamic mode decomposition…

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…

Dynamical systems are ubiquitous and are often modeled using a non-linear system of governing equations. Numerical solution procedures for many dynamical systems have existed for several decades, but can be slow due to high-dimensional…

The Dynamic Mode Decomposition (DMD)---a popular method for performing data-driven Koopman spectral analysis---has gained increased adoption as a technique for extracting dynamically meaningful spatio-temporal descriptions of fluid flows…

Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems' fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In…