Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exploiting symmetry for discrete-time reachability computations   We present a method of computing backward reachable sets for nonlinear
discrete-time control systems possessing continuous symmetries. The starting
point is a dynamic game formulation of reachability analysis where control
inputs aim to maintain the state variables within a target tube despite
disturbances. Our method exploits symmetry to compute the reachable sets in a
lower-dimensional space, enabling a significant computational speedup. To
achieve this, we present a general method for symmetry reduction based on the
Cartan frame, which simplifies the dynamic programming iteration without
algebraic manipulation of the state update equations. We illustrate the results
by computing a backward reachable set for a six-dimensional reach-avoid game of
two Dubins vehicles.

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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: supr-con