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second update JOSS
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pswpswpsw committed Oct 6, 2023
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Expand Up @@ -73,7 +73,7 @@ The core component of the PyKoopman package is the Koopman model class. The exte

As illustrated in Fig. \ref{fig:koopman-formalism}, `PyKoopman` is designed to lift nonlinear dynamics into a linear system with linear actuation. Specifically, our `PyKoopman` implementation involves two major steps:

![{Broad categorization of model types that can be identified with current `PyKoopman`. While the dotted parts (marked with ``$\cdot$'') can be simultaneously discovered within the framework, they are typically ignored for control purposes.\label{fig:koopman-formalism}](Fig3.png){ width=40% }
![Broad categorization of model types that can be identified with current `PyKoopman`. While the dotted parts (marked with ``$\cdot$'') can be simultaneously discovered within the framework, they are typically ignored for control purposes.\label{fig:koopman-formalism}](Fig3.png){ width=40% }

- `observables`: the nonlinear observables used to lift $\mathbf{x}$ to $\mathbf{z}$, and reconstruct $\mathbf{x}$ from $\mathbf{z}$;
- `regression`: the regression used to find the optimal $\mathbf{A}$.
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