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Linear Avoidance in the Case of Interaction of Controlled Objects Groups

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Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 3))

Abstract

In this paper we study a conflict interaction of n pursuers and m evaders in Euclidean space Rk. All objects are linear and of the same type. The qualitative conclusion about avoidance problem solvability is developed depending on the ratio of numbers n, m and k. The avoidance problem from given initial states is considered as auxiliary. The results have a bearing on the research reported in [1–7].

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References

  1. L. S. Pontryagin and E. F. Mischenko, Avoidance Problem in Linear Differential Games, Dif. Uravn. 7 (1971), 436–445. [in Russian]

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  2. N. N. Petrov and N. N. Petrov, On a Differential Game of “Cossacks-Robbers”, Dif. Uravn. 19 (1983), 1366–1374. [in Russian]

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  3. P. V. Prokopovich and A. A. Chikrii, A Problem of Interaction of Groups of Controlled Objects, in Theory of Optimal Solutions, Institute of Cybernetics, Kiev, 1987, 71–75. [in Russian]

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  4. A. A. Chikrii and P. V. Prokopovich, Pursuit and Evasion Problem for Interacting Groups of Moving Objects, Cybernetics, 25 (1989), 634– 640.

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  5. P. V. Prokopovich and A. A. Chikrii, Quasi-linear Conflict- controlled Processes with Non-fixed Time, Prikladnaya Matematika i Mekhanika, 55 (1991), 63–71. [in Russian]

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  6. A. A. Chikrii and P. V. Prokopovich, Simple Pursuit of One Evader by a Group, Cybernetics and Systems Analysis, 28 (1992), 438–444.

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  7. A. A. Chikrii and P. V. Prokopovich, Evasion Problem for Interacting Groups of Linear Objects, Doklady Academii Nauk SSSR, 333 (1993), 7352–739. [in Russian]

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© 1995 Birkhäuser Boston

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Chikrii, A.A., Prokopovich, P.V. (1995). Linear Avoidance in the Case of Interaction of Controlled Objects Groups. In: Olsder, G.J. (eds) New Trends in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 3. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4274-1_13

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  • DOI: https://doi.org/10.1007/978-1-4612-4274-1_13

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8719-3

  • Online ISBN: 978-1-4612-4274-1

  • eBook Packages: Springer Book Archive

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