Geodesic
The value function of a differential game with simple motions and an integro-terminal cost
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 124, pp. 877-890

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An antagonistic positional differential game of two persons is considered. The dynamics of the system is described by a differential equation with simple motions, and the payoff functional is integro-terminal. For the case when the terminal function and the Hamiltonian are piecewise linear, and the dimension of the state space is two, a finite algorithm for the exact construction of the value function is proposed.
Keywords: differential game, value function, Hamilton-Jacobi equation, algorithm.
Mots-clés : simple motions 
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     author = {L. G. Shagalova},
     title = {The value function of a differential game with simple motions and an integro-terminal cost},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {877--890},
     publisher = {mathdoc},
     volume = {23},
     number = {124},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2018_23_124_a29/}
}
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L. G. Shagalova. The value function of a differential game with simple motions and an integro-terminal cost. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 124, pp. 877-890. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_124_a29/