Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discovering conservation laws from data for control   Conserved quantities, i.e. constants of motion, are critical for
characterizing many dynamical systems in science and engineering. These
quantities are related to underlying symmetries and they provide fundamental
knowledge about physical laws, describe the evolution of the system, and enable
system reduction. In this work, we formulate a data-driven architecture for
discovering conserved quantities based on Koopman theory. The Koopman operator
has emerged as a principled linear embedding of nonlinear dynamics, and its
eigenfunctions establish intrinsic coordinates along which the dynamics behave
linearly. Interestingly, eigenfunctions of the Koopman operator associated with
vanishing eigenvalues correspond to conserved quantities of the underlying
system. In this paper, we show that these invariants may be identified with
data-driven regression and power series expansions, based on the infinitesimal
generator of the Koopman operator. We further establish a connection between
the Koopman framework, conserved quantities, and the Lie-Poisson bracket. This
data-driven method for discovering conserved quantities is demonstrated on the
three-dimensional rigid body equations, where we simultaneously discover the
total energy and angular momentum and use these intrinsic coordinates to
develop a model predictive controller to track a given reference value.

17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn