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Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…
The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow…
Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the…
The Koopman operator has gained significant attention in recent years for its ability to verify evolutionary properties of continuous-time nonlinear systems by lifting state variables into an infinite-dimensional linear vector space. The…
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…
This paper proposes a method for uncertainty quantification of an autoencoder-based Koopman operator. The main challenge of using the Koopman operator is to design the basis functions for lifting the state. To this end, this paper builds an…
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…
This paper proposes a data-driven framework to learn a finite-dimensional approximation of a Koopman operator for approximating the state evolution of a dynamical system under noisy observations. To this end, our proposed solution has two…
In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to…
The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept$\unicode{x2013}$representing highly nonlinear dynamical systems by infinite-dimensional linear…
A popular technique used to obtain linear representations of nonlinear systems is the so-called Koopman approach, where the nonlinear dynamics are lifted to a (possibly infinite dimensional) linear space through nonlinear functions called…
We propose a noise-robust learning framework for the Koopman operator of nonlinear dynamical systems, with guaranteed long-term stability and improved model performance for better model-based predictive control tasks. Unlike some existing…
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,…
In this work, we propose a meta-learning-based Koopman modeling and predictive control approach for nonlinear systems with parametric uncertainties. An adaptive deep meta-learning-based modeling approach, called Meta Adaptive Koopman…
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 presents a new data-driven controller synthesis based on the Koopman operator and the extended $\mathcal{H}_2$ norm characterization of discrete-time linear systems. We model dynamical systems as polytope sets which are derived…
This paper proposes an Extended-Kalman-Filter-like observer for parameter estimation during synchronization of chaotic systems. The exponential stability of the observer is guaranteed by a persistent excitation condition. This approach is…
We propose a novel operator-theoretic framework to study global stability of nonlinear systems. Based on the spectral properties of the so-called Koopman operator, our approach can be regarded as a natural extension of classic linear…
The article is devoted to the problem of synthesis of observers of state variables for linear stationary objects operating under conditions of noise or disturbances in the measurement channel. The paper considers a fully observable linear…
Providing rigorous reachability guarantees for unknown complex systems is a crucial and challenging task. In this paper, we present a novel data-driven framework that addresses this challenge by leveraging Koopman operator theory. Instead…