Let and be an action spaces for.
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- Differential Game Theory;
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A linear differential game is expressed as. The original work of Isaacs [ ] contains many interesting examples of pursuit-evasion differential games. One of the most famous is described next.
Both exist in the same world,. The speeds of the car and robot are and , respectively. It is assumed that , which means that the pursuer moves faster than the evader. The transition equation is given by extending The task is to determine whether the pursuer can come within some prescribed distance of the evader:. Another interesting pursuit-evasion game arises in the case of one car attempting to intercept another [ ].
Each has a transition equation given by The state transition equation for the game is. Next: Further Reading Up: Bakolas E, Tsiotras P On the relay pursuit of a maneuvering target by a group of pursuers. Birkhauser, Boston, pp — Google Scholar. Botkin ND, Ryazantseva EA Algorithm of constructing the solvability set for linear differential games of high dimension.
Optimization, estimation and control. In: Proceedings of the 14th European control conference, pp — Google Scholar. Chikrii AA On the evasion problem in a linear differential game.
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Autom Rem Control 38 9 — Google Scholar. Chikrii AA Conflict controlled processes. Chikrii AA Conflict-controlled processes, mathematics and its applications, vol Fisac JF, Sastry S The pursuit-evasion-defense differential game in dynamic constrained environments. Grigorenko NL On a quasilinear problem of pursuit by several objects. Grigorenko NL Mathematical methods of control of multiple dynamic processes. Isaacs R Differential games.
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In: Advances in aerospace guidance, navigation and control. Springer, Berlin, Heidelberg, pp — Google Scholar. Interval analysis interpretation. In: Altman E, Pourtallier O eds Annals of the international society of dynamic games: advances in dynamic games and applications, vol 6. Kurzhanski AB On a team control problem under obstacles. Kurzhanski AB Problem of collision avoidance for a team motion with obstacles.
Levchenkov AY, Pashkov AG Differential game of optimal approach of two inertial pursuers to a noninertial evader. Mikhalev DK, Ushakov VN Two algorithms for approximate construction of the set of positional absorption in the game problem of pursuit. Patsko VS, Turova VL Level sets of the value function in differential games with the homicidal chauffeur dynamics. Sov Math Dokl — Google Scholar. Petrosyan LA The multi-person lifeline games of pursuit.
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- Pursuit-Evasion Differential Games!
Petrosyan LA Differential games of pursuit. Petrov NN A group pursuit problem with phase constraints. Pontryagin LS Linear differential games, 1.