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A Method of Solving Differential Games Under Integrally Constrained Controls

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Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 12))

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Abstract

This study deals with linear game problems under integral constraints on controls. The proposed scheme leans upon the ideas of the method of resolving functions [Chikrii, Conflict Controlled Processes. Kluwer, Boston (1997)]. The analog of the Pontryagin condition formulated in the paper, makes it feasible to derive sufficient conditions for the finite-time termination of differential game. Obtained results are illustrated with the typical game state of affairs “simple motion” and continue researches [Chikrii and Belousov, Mem. Inst. Math. Mech. Ural Div. Russ. Acad. Sci. 15(4):290–301 (2009) (in Russian); Nikol’sky, Diff. Eq. Minsk. 8(6):964–971 (1972) (in Russian); Subbotin and Chentsov, Optimization of Guarantee in Problems of Control. Nauka, Moscow (1981) (in Russian)].

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References

  1. Chikrii, A.A.: Conflict Controlled Processes. Kluwer, Boston (1997)

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  2. Kisielewicz M.: Differential Inclusions and Optimal Control. Kluwer, Boston (1991)

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Author information

Authors and Affiliations

  1. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    Aleksandr A. Belousov & Arkadii A. Chikrii

  2. Ural Division of Russian Academy of Sciences, Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Aleksander G. Chentsov

Authors
  1. Aleksandr A. Belousov
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  2. Aleksander G. Chentsov
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  3. Arkadii A. Chikrii
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Corresponding author

Correspondence to Aleksandr A. Belousov .

Editor information

Editors and Affiliations

  1. , CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris, 75775, France

    Pierre Cardaliaguet

  2. Wilfrid Laurier University, University Ave W 75, Waterloo, N2L 3C5, Ontario, Canada

    Ross Cressman

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Belousov, A.A., Chentsov, A.G., Chikrii, A.A. (2013). A Method of Solving Differential Games Under Integrally Constrained Controls. In: Cardaliaguet, P., Cressman, R. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8355-9_16

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