Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamic Feedback Linearization of Control Systems with Symmetry   Control systems of interest are often invariant under Lie groups of
transformations. Given such a control system, assumed to not be static feedback
linearizable, a verifiable geometric condition is described and proven to
guarantee its dynamic feedback linearizability. Additionally, a systematic
procedure for obtaining all the system trajectories is shown to follow from
this condition. Besides smoothness and the existence of symmetry, no further
assumption is made on the local form of a control system, which is therefore
permitted to be fully nonlinear and time varying. Likewise, no constraints are
imposed on the local form of the dynamic compensator. Particular attention is
given to those systems requiring non-trivial dynamic extensions; that is,
beyond augmentation by chains of integrators. Nevertheless, the results are
illustrated by an example of each type. Firstly, a control system that can be
dynamically linearized by a chain of integrators, and secondly, one which does
not possess any linearizing chains of integrators and for which a dynamic
feedback linearization is nevertheless derived. These systems are discussed in
some detail. The constructions have been automated in the Maple package
DifferentialGeometry.

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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th