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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…

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…

This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic…

This paper proposes a consensus-based distributed nonlinear filter with kernel mean embedding (KME). This fills with gap of posterior density approximation with KME for distributed nonlinear dynamic systems. To approximate the posterior…

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,…

We derive novel deterministic bounds on the approximation error of data-based bilinear surrogate models for unknown nonlinear systems. The surrogate models are constructed using kernel-based extended dynamic mode decomposition to…

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 Koopman operator, as a linear representation of a nonlinear dynamical system, has been attracting attention in many fields of science. Recently, Koopman operator theory has been combined with another concept that is popular in data…

This paper proposes a new method to propagate uncertainties undergoing nonlinear dynamics using the Koopman Operator (KO). Probability density functions are propagated directly using the Koopman approximation of the solution flow of the…

The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework naturally yields linear embedding models, there have been…

In this work, we consider a state estimation problem for large-scale nonlinear processes in the absence of first-principles process models. By exploiting process operation data, both process modeling and state estimation design are…

The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through…

Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…

Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…

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…

This paper develops a methodology for adaptive data-driven Model Predictive Control (MPC) using Koopman operators. While MPC is ubiquitous in various fields of engineering, the controller performance can deteriorate if the modeling error…

In this draft, fault diagnosis in nonlinear dynamic systems is addressed. The objective of this work is to establish a framework, in which not only model-based but also data-driven and machine learning based fault diagnosis strategies can…

Ambiguity sets of probability distributions are used to hedge against uncertainty about the true probabilities of random quantities of interest (QoIs). When available, these ambiguity sets are constructed from both data (collected at the…

This work establishes a rigorous bridge between infinite-dimensional delay dynamics and finite-dimensional Koopman learning, with explicit and interpretable error guarantees. While Koopman analysis is well-developed for ordinary…

Mobile robot navigation can be challenged by system uncertainty. For example, ground friction may vary abruptly causing slipping, and noisy sensor data can lead to inaccurate feedback control. Traditional model-based methods may be limited…