Related papers: The Koopman Expectation: An Operator Theoretic Met…
This paper presents a data-driven method to find a closed-loop optimal controller, which minimizes a specified infinite-horizon cost function for systems with unknown dynamics. Suppose the closed-loop optimal controller can be parameterized…
This paper presents an interpretable machine learning approach that characterizes load dynamics within an operator-theoretic framework for electricity load forecasting in power grids. We represent the dynamics of load data using the Koopman…
Dynamical systems have a wide range of applications in mechanics, electrical engineering, chemistry, and so on. In this work, we propose the adaptive spectral Koopman (ASK) method to solve nonlinear autonomous dynamical systems. This novel…
In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust…
Autonomous Underwater Vehicles (AUVs) play an essential role in modern ocean exploration, and their speed control systems are fundamental to their efficient operation. Like many other robotic systems, AUVs exhibit multivariable nonlinear…
Machine learning methods allow the prediction of nonlinear dynamical systems from data alone. The Koopman operator is one of them, which enables us to employ linear analysis for nonlinear dynamical systems. The linear characteristics of the…
Although Koopman operators provide a global linearization for autonomous dynamical systems, nonautonomous systems are not globally linear in the inputs. State (or output) feedback controller design therefore remains nonconvex in typical…
The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems. The main reason is the enormous potential of identifying linear function space representations of nonlinear dynamics from…
This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman…
Shipboard carbon capture is a promising solution to help reduce carbon emissions in international shipping. In this work, we propose a data-driven dynamic modeling and economic predictive control approach within the Koopman framework. This…
The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a…
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…
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…
We develop algorithms built around properties of the transfer operator and Koopman operator which 1) test for possible multiscale dynamics in a given dynamical system, 2) estimate the magnitude of the time-scale separation, and finally 3)…
We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…
The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional…
Data-driven model predictive control based on Willems' fundamental lemma has proven effective for linear systems, but extending stability guarantees to nonlinear systems remains an open challenge. In this paper, we establish conditions…
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…
Koopman-based learning methods can potentially be practical and powerful tools for dynamical robotic systems. However, common methods to construct Koopman representations seek to learn lifted linear models that cannot capture nonlinear…
A learning method is proposed for Koopman operator-based models with the goal of improving closed-loop control behavior. A neural network-based approach is used to discover a space of observables in which nonlinear dynamics is linearly…