Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A discrete-time Pontryagin maximum principle on matrix Lie groups   In this article we derive a Pontryagin maximum principle (PMP) for
discrete-time optimal control problems on matrix Lie groups. The PMP provides
first order necessary conditions for optimality; these necessary conditions
typically yield two point boundary value problems, and these boundary value
problems can then solved to extract optimal control trajectories. Constrained
optimal control problems for mechanical systems, in general, can only be solved
numerically, and this motivates the need to derive discrete-time models that
are accurate and preserve the non-flat manifold structures of the underlying
continuous-time controlled systems. The PMPs for discrete-time systems evolving
on Euclidean spaces are not readily applicable to discrete-time models evolving
on non-flat manifolds. In this article we bridge this lacuna and establish a
discrete-time PMP on matrix Lie groups. Our discrete-time models are derived
via discrete mechanics, (a structure preserving discretization scheme,) leading
to the preservation of the underlying manifold over time, thereby resulting in
greater numerical accuracy of our technique. This PMP caters to a class of
constrained optimal control problems that includes point-wise state and control
action constraints, and encompasses a large class of control problems that
arise in various field of engineering and the applied sciences.

16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph