Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation of linear controlled dynamical systems with small random
  noise and fast periodic sampling   In this paper, we study the dynamics of a linear control system with given
state feedback control law in the presence of fast periodic sampling at
temporal frequency $1/\delta$ ($0 < \delta \ll 1$), together with small white
noise perturbations of size $\varepsilon$ ($0<\varepsilon \ll 1$) in the state
dynamics. For the ensuing continuous-time stochastic process indexed by two
small parameters $\varepsilon,\delta$, we obtain effective ordinary and
stochastic differential equations describing the mean behavior and the typical
fluctuations about the mean in the limit as $\varepsilon,\delta \searrow 0$.
The effective fluctuation process is found to vary, depending on whether
$\delta \searrow 0$ faster than/at the same rate as/slower than $\varepsilon
\searrow 0$. The most interesting case is found to be the one where
$\delta,\varepsilon$ are comparable in size; here, the limiting stochastic
differential equation for the fluctuations has both a diffusive term due to the
small noise and an effective drift term which captures the cumulative effect of
the fast sampling. In this regime, our results yield a time-inhomogeneous
Markov process which provides a strong (pathwise) approximation of the original
non-Markovian process, together with estimates on the ensuing error. A simple
example involving an infinite time horizon linear quadratic regulation problem
illustrates the results.

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The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg