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A differential game of approach with two pursuers and one evader

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Abstract

A differential game of approach with one evader and two pursuers with a nonconvex payoff function is considered. The duration of the game is fixed. The payoff functional is the distance between the object being pursued and the pursuer closest to it when the game terminates. An explicit form of the game value is found for all possible game positions. The paper is closely related to Refs. 1–12.

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References

  1. Isaacs, R.,Differential Games, John Wiley and Sons, New York, New York, 1965.

    Google Scholar 

  2. Krasovskii, N. N., andSubbotin, A. I.,Positional Differential Games, Nauka, Moscow, 1974 (in Russian).

    Google Scholar 

  3. Krasovskii, N. N.,Differential Games: Approximation and Formal Models, Mathematicheskie Sbornik, Vol. 107, No. 4, pp. 541–571, 1978 (in Russian).

    Google Scholar 

  4. Subbotin, A. I.,Generalization of the Main Equation of Differential Game Theory, Journal of Optimization Theory and Applications, Vol. 43, No. 1, pp. 103–133, 1984.

    Google Scholar 

  5. Subbotin, A. I., andChentzov, A. G.,Optimization of Guaranteed Result in Control Problems, Nauka, Moscow, 1981 (in Russian).

    Google Scholar 

  6. Hagedorn, P., andBreakwell, J. V.,A Differential Game with Two Pursuers and One Evader, Journal of Optimization Theory and Applications, Vol. 18, No. 1, pp. 15–29, 1976.

    Google Scholar 

  7. Melikyan, A. A.,Optimal Interaction of Two Pursuers in a Game, Izvestiya Akademii Nauk SSSR, Tekhnicheskaya Kibernetika, No. 2, pp. 49–56, 1981 (in Russian).

  8. Grigorenko, N. L.,Pursuit of an Evader by Several Pursuers of Different Types, Soviet Mathematics Doklady, Vol. 268, No. 3, pp. 529–533, 1983.

    Google Scholar 

  9. Pshenichnyi, B. N., Chikrii, A. A., andRappoport, I. S.,An Efficient Method of Solving Differential Games with Many Pursuers, Soviet Mathematics Doklady, Vol. 256, No. 3, pp. 530–535, 1981.

    Google Scholar 

  10. Pashkov, A. G., andTerekhov, S. D.,On a Game of Optimal Pursuit of an Evader by Two Pursuers, Prikladnaya Mathematika i Mekhanika, Vol. 47, No. 6, pp. 898–903, 1983 (in Russian).

    Google Scholar 

  11. Levchenkov, A. Y., andPashkov, A. G.,A Game of Optimal Approach with Two Inertial Pursuers and a Noninertial Evader, Prikladnaya Matematika i Mekhanika, Vol. 49, No. 4, pp. 536–547, 1985 (in Russian).

    Google Scholar 

  12. Levchenkov, A. Y., Pashkov, A. G., andTerekhov, S. D.,Differential Games of Encounter of an Evader by Two Dynamical Pursuers, Institute for Problems in Mechanics, Moscow, USSR, Preprint No. 266, 1985 (in Russian).

    Google Scholar 

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Communicated by N. V. Banichuk

The authors would like to thank Professor A. I. Subbotin for his valuable advice and encouragement.

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Pashkov, A.G., Terekhov, S.D. A differential game of approach with two pursuers and one evader. J Optim Theory Appl 55, 303–311 (1987). https://doi.org/10.1007/BF00939087

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