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Discontinuous Value Function in Time-Optimal Differential Games

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Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 11))

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Abstract

The article is devoted to the study of the value function in time-optimal differential games. Suppose that some function to be tested is constructed. It is required to prove that this function coincides with the value function of the game. A theorem on sufficient conditions for a tested function to coincide with the value function of the time-optimal differential game under consideration is proved. The theorem covers the case of a discontinuous value function. An application of the theorem is illustrated by an example of a time-optimal second-order differential game with the dynamics of conflict-controlled material point.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, S.Kovalevskaya str., 16, GSP-384, 620219, Ekaterinburg, Russia

    Liudmila Kamneva

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  1. Liudmila Kamneva
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Correspondence to Liudmila Kamneva .

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Editors and Affiliations

  1. , HEC Montréal, Department of Management Science, 3000 Chemin de la Côte-Sainte-Catherine, Montreal, H3T2A7, Canada

    Michèle Breton

  2. Wrocław University of Technology, Institute of Mathematics and Computer Sc, Wybrzeże Wyspiańskiego 27, Wrocław, PL-50-370, Poland

    Krzysztof Szajowski

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Kamneva, L. (2011). Discontinuous Value Function in Time-Optimal Differential Games. In: Breton, M., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 11. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8089-3_6

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