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SCIENTIA SINICA Informationis, Volume 49 , Issue 11 : 1488-1501(2019) https://doi.org/10.1360/N112018-00048

Control of asynchronous sequential machine with adversarial input based on the semi-tensor product of matrices

More info
  • ReceivedMar 9, 2018
  • AcceptedDec 27, 2018
  • PublishedNov 14, 2019

Abstract


Funded by

国家自然科学基金(61573199)

天津市自然科学基金(14JCYBJC18700)


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  • Figure 1

    The closed-loop system ${\Sigma~_{\left|~C~\right.}}$ with an adversarial input

  • Table 1   The stable transition functions and output functions of machine $\Sigma$
    $s$ $(a,\alpha~)$ $(a,\beta~)$ $(b,\alpha~)$ $(b,\beta~)$ $(c,\alpha~)$ $(c,\beta~)$ $(c,\alpha~)$ $(d,\beta~)$ $h$ $X$
    ${x_1}$ ${x_2}$ ${x_4}$ ${x_1}$ ${x_1}$ ${x_1}$
    ${x_2}$ ${x_2}$ ${x_2}$ ${x_4}$ ${x_3}$ ${x_3}$ ${x_2}$ ${x_1}$ ${x_2}$ ${x_2}$
    ${x_3}$ ${x_2}$ ${x_3}$ ${x_3}$ ${x_4}$ ${x_4}$ ${x_3}$ ${x_3}$
    ${x_4}$ ${x_2}$ ${x_2}$ ${x_4}$ ${x_3}$ ${x_3}$ ${x_4}$ ${x_4}$ ${x_4}$ ${x_4}$
  • Table 2   The stable transition functions and output functions of machine $\Sigma~'$
    $s'$ $a$ $b$ $c$ $d$ $h'$ $X$
    ${{x}_1}$ ${{x}_2}$ ${{x}_4}$ ${{x}_1}$ ${x_1}$ ${x_1}$
    ${{x}_2}$ ${{x}_2}$ ${{x}_3}$ ${{x}_2}$ ${{x}_4}$ ${x_2}$ ${x_2}$
    ${{x}_3}$ ${{x}_3}$ ${{x}_3}$ ${{x}_4}$ ${x_3}$ ${x_3}$
    ${{x}_4}$ ${{x}_2}$ ${{x}_4}$ ${{x}_3}$ ${{x}_4}$ ${x_4}$ ${x_4}$