Data-driven discovery of Koopman eigenfunctions for control
Data-driven transformations that reformulate nonlinear systems in a linear framework have
the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics …
the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics …
[HTML][HTML] Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control
In this work, we explore finite-dimensional linear representations of nonlinear dynamical
systems by restricting the Koopman operator to an invariant subspace spanned by specially …
systems by restricting the Koopman operator to an invariant subspace spanned by specially …
Koopman operator dynamical models: Learning, analysis and control
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 …
Physics-informed probabilistic learning of linear embeddings of nonlinear dynamics with guaranteed stability
S Pan, K Duraisamy - SIAM Journal on Applied Dynamical Systems, 2020 - SIAM
The Koopman operator has emerged as a powerful tool for the analysis of nonlinear
dynamical systems as it provides coordinate transformations to globally linearize the …
dynamical systems as it provides coordinate transformations to globally linearize the …
[HTML][HTML] Deep learning for universal linear embeddings of nonlinear dynamics
Identifying coordinate transformations that make strongly nonlinear dynamics approximately
linear has the potential to enable nonlinear prediction, estimation, and control using linear …
linear has the potential to enable nonlinear prediction, estimation, and control using linear …
[图书][B] Koopman operator in systems and control
As an example of fruitful cross-fertilization between mathematics and engineering, nonlinear
control theory has attracted considerable effort driven by the need to understand, predict …
control theory has attracted considerable effort driven by the need to understand, predict …
Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
We derive a data-driven method for the approximation of the Koopman generator called
gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic …
gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic …
Learning compositional koopman operators for model-based control
Finding an embedding space for a linear approximation of a nonlinear dynamical system
enables efficient system identification and control synthesis. The Koopman operator theory …
enables efficient system identification and control synthesis. The Koopman operator theory …
Extended dynamic mode decomposition with learned Koopman eigenfunctions for prediction and control
This paper presents a novel learning framework to construct Koopman eigenfunctions for
unknown, nonlinear dynamics using data gathered from experiments. The learning …
unknown, nonlinear dynamics using data gathered from experiments. The learning …
Optimal construction of Koopman eigenfunctions for prediction and control
This article presents a novel data-driven framework for constructing eigenfunctions of the
Koopman operator geared toward prediction and control. The method leverages the …
Koopman operator geared toward prediction and control. The method leverages the …