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The Koopman operator framework can be used to identify a data-driven model of a nonlinear system. Unfortunately, when the data is corrupted by noise, the identified model can be biased. Additionally, depending on the choice of lifting…
Extended Dynamic Mode Decomposition (EDMD) is a widely-used data-driven approach to learn an approximation of the Koopman operator. Consequently, it provides a powerful tool for data-driven analysis, prediction, and control of nonlinear…
This paper presents a class of linear predictors for nonlinear controlled dynamical systems. The basic idea is to lift the nonlinear dynamics into a higher dimensional space where its evolution is approximately linear. In an uncontrolled…
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 Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data. Building on the recent development of the Koopman model…
Koopman operator has been recognized as an ongoing data-driven modeling method for vehicle dynamics which lifts the original state space into a high-dimensional linear state space. The deep neural networks (DNNs) are verified to be useful…
We propose a novel framework for safe navigation in dynamic environments by integrating Koopman operator theory with conformal prediction. Our approach leverages data-driven Koopman approximation to learn nonlinear dynamics and employs…
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…
Gas turbine engines are complex and highly nonlinear dynamical systems. Deriving their physics-based models can be challenging because it requires performance characteristics that are not always available, often leading to many simplifying…
We propose an alternating optimization algorithm to the nonconvex Koopman operator learning problem for nonlinear dynamic systems. We show that the proposed algorithm will converge to a critical point with rate $O(1/T)$ and $O(\frac{1}{\log…
Achieving rapid and time-deterministic stabilization for complex systems characterized by strong nonlinearities and parametric uncertainties presents a significant challenge. Traditional model-based control relies on precise system models,…
Analyzing the inner mechanisms of deep neural networks is a fundamental task in machine learning. Existing work provides limited analysis or it depends on local theories, such as fixed-point analysis. In contrast, we propose to analyze…
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…
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…
Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of…
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…
Recent advances in diffusion-based robot policies have demonstrated significant potential in imitating multi-modal behaviors. However, these approaches typically require large quantities of demonstration data paired with corresponding robot…
An efficient way to control systems with unknown nonlinear dynamics is to find an appropriate embedding or representation for simplified approximation (e.g. linearization), which facilitates system identification and control synthesis.…
The Koopman operator is an useful analytical tool for studying dynamical systems -- both controlled and uncontrolled. For example, Koopman eigenfunctions can provide non-local stability information about the underlying dynamical system.…
We introduce two novel generalizations of the Koopman operator method of nonlinear dynamic modeling. Each of these generalizations leads to greatly improved predictive performance without sacrificing a unique trait of Koopman methods: the…