Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal construction of Koopman eigenfunctions for prediction and
  control   This work presents a novel data-driven framework for constructing
eigenfunctions of the Koopman operator geared toward prediction and control.
The method leverages the richness of the spectrum of the Koopman operator away
from attractors to construct a rich set of eigenfunctions such that the state
(or any other observable quantity of interest) is in the span of these
eigenfunctions and hence predictable in a linear fashion. The eigenfunction
construction is optimization-based with no dictionary selection required. Once
a predictor for the uncontrolled part of the system is obtained in this way,
the incorporation of control is done through a multi-step prediction error
minimization, carried out by a simple linear least-squares regression. The
predictor so obtained is in the form of a linear controlled dynamical system
and can be readily applied within the Koopman model predictive control
framework of [12] to control nonlinear dynamical systems using linear model
predictive control tools. The method is entirely data-driven and based purely
on convex optimization, with no reliance on neural networks or other non-convex
machine learning tools. The novel eigenfunction construction method is also
analyzed theoretically, proving rigorously that the family of eigenfunctions
obtained is rich enough to span the space of all continuous functions. In
addition, the method is extended to construct generalized eigenfunctions that
also give rise Koopman invariant subspaces and hence can be used for linear
prediction. Detailed numerical examples with code available online demonstrate
the approach, both for prediction and feedback control.

15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
1
The categories of this paper are: cs