Geodesic
Numerical Study of a Linear Differential Game with Two Pursuers and One Evader
Contributions to game theory and management, Tome 4 (2011), pp. 154-171

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A linear pursuit-evasion differential game with two pursuers and one evader is considered. The pursuers try to minimize the final miss (an ideal situation is to get exact capture), the evader counteracts them. Two case are investigated. In the first case, each one pursuer is dynamically stronger than the evader, in the second one, they are weaker. Results of numerical study of value function level sets (Lebesgue sets) for these cases are given. A method for constructing optimal feedback controls is suggested on the basis of switching lines. Results of numerical simulation are shown.
Keywords: pursuit-evasion differential game, linear dynamics, value function, optimal feedback control. 
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     author = {Sergey S. Ganebny and Sergey S. Kumkov and St\'ephane Le M\'enec and Valerii S. Patsko},
     title = {Numerical {Study} of a {Linear} {Differential} {Game} with {Two} {Pursuers} and {One} {Evader}},
     journal = {Contributions to game theory and management},
     pages = {154--171},
     publisher = {mathdoc},
     volume = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2011_4_a11/}
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Sergey S. Ganebny; Sergey S. Kumkov; Stéphane Le Ménec; Valerii S. Patsko. Numerical Study of a Linear Differential Game with Two Pursuers and One Evader. Contributions to game theory and management, Tome 4 (2011), pp. 154-171. http://geodesic.mathdoc.fr/item/CGTM_2011_4_a11/