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A research contribution on an evasion problem

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Abstract

In the present research, we study an evasion differential game with finite number of pursuers and one evader in Hilbert space. The control functions of players are subject to the geometric constraints. We solve the game by presenting an strategy for the evader which guarantees its evasion.

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References

  1. Chikrii, A.A., Prokopovich, P.V.: Simple pursuit of one evader by a group. Cybern. Syst. Anal. 28(3), 438–444 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  2. Croft, H.T.: Lion and man: a postscript. J. Lond. Math. Soc. 39, 385–390 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  3. Flynn, J.: Lion and man: the boundary constraint. SIAM J. Control 11, 397–411 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ibragimov, G.I., Salimi, M.: Pursuit-evasion differential game with many inertial players. Mathematical Problems in Engineering (2009) (Article ID 653723)

  5. Ibragimov, G.I., Salimi, M., Amini, M.: Evasion from many pursuers in simple motion differential game with integral constraints. Eur. J. Oper. Res. 218, 505–511 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Isaacs, R.: Differential Games. Wiley, New York (1965)

    MATH  Google Scholar 

  7. Ivanov, R.P.: Simple pursuit-evasion on a compact convex set. Dokl. Akad. Nauk SSSR 254(6), 1318–1321 (1980)

    MathSciNet  Google Scholar 

  8. Petrosyan, L.A.: Differential Pursuit Games. Izdat Leningrad University, Leningrad (1977)

    MATH  Google Scholar 

  9. Pshenichii, B.N.: Simple pursuit by several objects. Cybern. Syst. Anal. 12(3), 145–146 (1976)

    MathSciNet  Google Scholar 

  10. Salimi, M., Ibragimov, G.I., Siegmund, S., Sharifi, S.: On a fixed duration pursuit differential game with geometric and integral constraints. Dyn. Games Appl. 6(3), 409–425 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Center for Dynamics, Department of Mathematics, Technische Universität Dresden, 01062, Dresden, Germany

    Mehdi Salimi

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  1. Mehdi Salimi
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Correspondence to Mehdi Salimi.

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Salimi, M. A research contribution on an evasion problem. SeMA 75, 139–144 (2018). https://doi.org/10.1007/s40324-017-0122-4

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  • DOI: https://doi.org/10.1007/s40324-017-0122-4

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