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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

In this study, we investigate the control problem of asynchronous sequential machine with adversarial input by using the semi-tensor product (STP) of matrices. First, by applying the STP of matrices, a new algebraic expression of asynchronous sequential machines with an adversarial input is deduced. Next, by investigating the control process, the controller with the minimal state set is designed, and two algorithms for assigning the values to the state transition structure matrix and the output structure matrix of the controller are proposed. Then, in the framework of the algebraic expression of the asynchronous sequential machines with adversarial input and two proposed algorithms, an algebra expression of the closed-loop system dynamic is established; the theoretical results are verified by using this algebra expression. Finally, an example is presented to illustrate the validity and application of the proposed approach.


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 $\Sigma~'$
    $s'$ $a$ $b$ $c$ $d$ $h'$ $X$
    ${{x}_1}$ ${{x}_2}$ ${{x}_4}$ ${{x}_1}$ ${x_1}$ ${x_1}$
    ${{x}_2}$ ${{x}_2}$ ${{x}_3}$ ${{x}_2}$ ${{x}_4}$ ${x_2}$ ${x_2}$
    ${{x}_3}$ ${{x}_3}$ ${{x}_3}$ ${{x}_4}$ ${x_3}$ ${x_3}$
    ${{x}_4}$ ${{x}_2}$ ${{x}_4}$ ${{x}_3}$ ${{x}_4}$ ${x_4}$ ${x_4}$

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