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Advances in Dynamic Games pp 315–325Cite as

Birkhäuser

A Method of Solving Differential Games Under Integrally Constrained Controls

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

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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  3. Kuratowski, K., Ryll-Nardzewski, C.: A general theorem on selectors. Bull. Acad. Pol. Sci. Warsaw 13, 397–403 (1965)

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  4. Pontryagin, L.S.: Selected Scientific Papers, vol. 2. Nauka, Moscow (1988) (in Russian)

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  5. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)

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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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