Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive Backstepping Control for Fractional-Order Nonlinear Systems
  with External Disturbance and Uncertain Parameters Using Smooth Control   In this paper, we consider controlling a class of single-input-single-output
(SISO) commensurate fractional-order nonlinear systems with parametric
uncertainty and external disturbance. Based on backstepping approach, an
adaptive controller is proposed with adaptive laws that are used to estimate
the unknown system parameters and the bound of unknown disturbance. Instead of
using discontinuous functions such as the $\mathrm{sign}$ function, an
auxiliary function is employed to obtain a smooth control input that is still
able to achieve perfect tracking in the presence of bounded disturbances.
Indeed, global boundedness of all closed-loop signals and asymptotic perfect
tracking of fractional-order system output to a given reference trajectory are
proved by using fractional directed Lyapunov method. To verify the
effectiveness of the proposed control method, simulation examples are
presented.

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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
2
The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg