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
Chikrii, A.A.: Conflict Controlled Processes. Kluwer, Boston (1997)
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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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DOI: https://doi.org/10.1007/978-0-8176-8355-9_16
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