Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Koopman Operator Based Modeling and Control of Rigid Body Motion
  Represented by Dual Quaternions   In this paper, we systematically derive a finite set of Koopman based
observables to construct a lifted linear state space model that describes the
rigid body dynamics based on the dual quaternion representation. In general,
the Koopman operator is a linear infinite dimensional operator, which means
that the derived linear state space model of the rigid body dynamics will be
infinite-dimensional, which is not suitable for modeling and control design
purposes. Recently, finite approximations of the operator computed by means of
methods like the Extended Dynamic Mode Decomposition (EDMD) have shown
promising results for different classes of problems. However, without using an
appropriate set of observables in the EDMD approach, there can be no guarantees
that the computed approximation of the nonlinear dynamics is sufficiently
accurate. The major challenge in using the Koopman operator for constructing a
linear state space model is the choice of observables. State-of-the-art methods
in the field compute the approximations of the observables by using neural
networks, standard radial basis functions (RBFs), polynomials or heuristic
approximations of these functions. However, these observables might not
providea sufficiently accurate approximation or representation of the dynamics.
In contrast, we first show the pointwise convergence of the derived observable
functions to zero, thereby allowing us to choose a finite set of these
observables. Next, we use the derived observables in EDMD to compute the lifted
linear state and input matrices for the rigid body dynamics. Finally, we show
that an LQR type (linear) controller, which is designed based on the truncated
linear state space model, can steer the rigid body to a desired state while its
performance is commensurate with that of a nonlinear controller. The efficacy
of our approach is demonstrated through numerical simulations.

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The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org