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On 0-Controllability and Pursuit Problems for Linear Discrete Systems Under Total Constraints on Controls

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International Conference on Mathematical Sciences and Statistics 2013

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Abstract

We consider linear discrete control and pursuit game problems. Control vectors are subjected to total constraints, which are discrete analogues of the integral constraint. By definition, (i) the control system is 0-controllable on the whole if there is a control such that the state of the system z(t) = 0 at some step t, (ii) pursuit can be completed if there exists a strategy of the pursuer such that for any strategy of the evader the state of the system y(t) = 0. We obtained sufficient condition for equivalence of 0-controllability and completion of the game from any initial position of the space.

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Acknowledgments

This research was partially supported by the Research Grant (RUGS) of the Universiti Putra Malaysia, No. 05-02-12-1868RU.

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Authors and Affiliations

  1. Institute of Mathematics, 29, Dorman yuli str., 100125, Tashkent, Uzbekistan

    Atamurat Kuchkarov & Akmal Sotvoldiev

  2. Institute for Mathematical Research, Universiti Putra Malaysia, 43400, Serdang, Selangor, Malaysia

    Gafurjan Ibragimov

Authors
  1. Atamurat Kuchkarov
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  2. Gafurjan Ibragimov
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  3. Akmal Sotvoldiev
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Corresponding author

Correspondence to Atamurat Kuchkarov .

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Editors and Affiliations

  1. University Putra Malaysia, Serdang, Selangor, Malaysia

    Adem Kilicman

  2. University Putra Malaysia, Serdang, Selangor, Malaysia

    Wah June Leong

  3. University Putra Malaysia, Serdang, Selangor, Malaysia

    Zainidin Eshkuvatov

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Kuchkarov, A., Ibragimov, G., Sotvoldiev, A. (2014). On 0-Controllability and Pursuit Problems for Linear Discrete Systems Under Total Constraints on Controls. In: Kilicman, A., Leong, W., Eshkuvatov, Z. (eds) International Conference on Mathematical Sciences and Statistics 2013. Springer, Singapore. https://doi.org/10.1007/978-981-4585-33-0_4

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