Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tight Decomposition Functions for Continuous-Time Mixed-Monotone Systems
  with Disturbances   The vector field of a mixed-monotone system is decomposable via a
decomposition function into increasing (cooperative) and decreasing
(competitive) components, and this decomposition allows for, e.g., efficient
computation of reachable sets and forward invariant sets. A main challenge in
this approach, however, is identifying an appropriate decomposition function.
In this work, we show that any continuous-time dynamical system with a
Lipschitz continuous vector field is mixed-monotone, and we provide a
construction for the decomposition function that yields the tightest
approximation of reachable sets when used with the standard tools for
mixed-monotone systems. Our construction is similar to that recently proposed
by Yang and Ozay for computing decomposition functions of discrete-time systems
[1] where we make appropriate modifications for the continuous-time setting and
also extend to the case with unknown disturbance inputs. As in [1], our
decomposition function construction requires solving an optimization problem
for each point in the state-space; however, we demonstrate through example how
tight decomposition functions can sometimes be calculated in closed form. As a
second contribution, we show how under-approximations of reachable sets can be
efficiently computed via the mixed-monotonicity property by considering the
backward-time dynamics.

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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org