Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local null controllability of the control-affine nonlinear systems with
  time-varying disturbances. Direct calculation of the null controllable region   The problem of local null controllability for the control-affine nonlinear
systems $\dot x(t)=f(x(t))+Bu(t)+w(t),$ $t\in[0,T]$ is considered in this
paper. The principal requirements on the system are that the LTI pair
$\left((\partial f/\partial x)(0), B\right)$ is controllable and the
disturbance is limited by the constraint $|f(0)+w(t)|\leq
M_d\left(1-\frac{t}{T}\right)^\eta,$ $M_d\geq0$ and $\eta>0.$ These properties
together with one technical assumption yield a complete answer to the problem
of deciding when the null controllable region have a nonempty interior. The
criteria obtained involve purely algebraic manipulations of vector field $f,$
input matrix $B$ and bound on the disturbance $w(t).$ To prove the main result
we have derived a new Gronwall-type inequality allowing the fine estimates of
the closed-loop solutions. The theory is illustrated and the efficacy of
proposed controller is demonstrated by the examples where the null controllable
region is explicitly calculated. Finally we established the sufficient
conditions to be the system under consideration (with $w(t)\equiv 0$) globally
null controllable.

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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org