Geodesic
Construction of solutions in certain differential games with phase constraints
Sbornik. Mathematics, Tome 196 (2005) no. 4, pp. 513-539 Cet article a éte moissonné depuis la source Math-Net.Ru

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A differential approach-evasion game with fixed termination time is studied. It is assumed that the phase vector of the conflict-control system is subjected to constraints that form a closed set in the position space. The ideology of stable bridges is used for solving the problem. A method of convolution is proposed, which is used in several problems for constructing explicitly the stable absorption operator defining the stable bridges. A method of approximate construction of the maximal stable bridge in this game is suggested. The relations are written down that define a system of sets approximating the maximal stable bridge, and a control procedure with a guide is described, which can be used for obtaining an approximate solution of the approach problem. 
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S. V. Grigor'eva; V. Yu. Pakhotinskikh; A. A. Uspenskii; V. N. Ushakov. Construction of solutions in certain differential games with phase constraints. Sbornik. Mathematics, Tome 196 (2005) no. 4, pp. 513-539. http://geodesic.mathdoc.fr/item/SM_2005_196_4_a2/

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