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Data-driven prediction in dynamical systems: recent developments
A Ghadami, BI Epureanu - Philosophical Transactions of …, 2022 - royalsocietypublishing.org
In recent years, we have witnessed a significant shift toward ever-more complex and ever-
larger-scale systems in the majority of the grand societal challenges tackled in applied …
larger-scale systems in the majority of the grand societal challenges tackled in applied …
Koopman operator dynamical models: Learning, analysis and control
P Bevanda, S Sosnowski, S Hirche - Annual Reviews in Control, 2021 - Elsevier
The Koopman operator allows for handling nonlinear systems through a globally linear
representation. In general, the operator is infinite-dimensional–necessitating finite …
representation. In general, the operator is infinite-dimensional–necessitating finite …
The multiverse of dynamic mode decomposition algorithms
MJ Colbrook - arxiv preprint arxiv:2312.00137, 2023 - arxiv.org
Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to
decompose complex, nonlinear systems into a set of modes, revealing underlying patterns …
decompose complex, nonlinear systems into a set of modes, revealing underlying patterns …
Multiplicative dynamic mode decomposition
N Boullé, MJ Colbrook - arxiv preprint arxiv:2405.05334, 2024 - arxiv.org
Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical
systems, facilitating the study of their spectral properties and enabling the prediction of the …
systems, facilitating the study of their spectral properties and enabling the prediction of the …
Data-driven approximations of dynamical systems operators for control
E Kaiser, JN Kutz, SL Brunton - The Koopman operator in systems and …, 2020 - Springer
Abstract The Koopman and Perron Frobenius transport operators are fundamentally
changing how we approach dynamical systems, providing linear representations for even …
changing how we approach dynamical systems, providing linear representations for even …
Feedback stabilization using Koopman operator
In this paper, we provide a systematic approach for the design of stabilizing feedback
controllers for nonlinear control systems using the Koopman operator framework. The …
controllers for nonlinear control systems using the Koopman operator framework. The …
The future of control of process systems
P Daoutidis, L Megan, W Tang - Computers & Chemical Engineering, 2023 - Elsevier
This paper provides a perspective on the major challenges and directions in academic
process control research over the next 5–10 years, and its industrial implementation. Large …
process control research over the next 5–10 years, and its industrial implementation. Large …
A convex approach to data-driven optimal control via Perron–Frobenius and Koopman operators
This article is about the data-driven computation of optimal control for a class of control affine
deterministic nonlinear systems. We assume that the control dynamical system model is not …
deterministic nonlinear systems. We assume that the control dynamical system model is not …
On robust computation of koopman operator and prediction in random dynamical systems
In the paper, we consider the problem of robust approximation of transfer Koopman and
Perron–Frobenius (P–F) operators from noisy time-series data. In most applications, the time …
Perron–Frobenius (P–F) operators from noisy time-series data. In most applications, the time …
Data-driven nonlinear stabilization using koopman operator
We propose the application of Koopman operator theory for the design of stabilizing
feedback controller for a nonlinear control system. The proposed approach is data-driven …
feedback controller for a nonlinear control system. The proposed approach is data-driven …