32,135 research outputs found
Pursuit-Evasion Differential Games with the Grönwall Type Constraints on Controls
A simple pursuit-evasion differential game of one pursuer and one evader is studied. The players' controls are subject to differential constraints in the form of the integral Grönwall inequality. The pursuit is considered completed if the state of the pursuer coincides with the state of the evader. The main goal of this work is to construct optimal strategies for the players and find the optimal pursuit time. A parallel approach strategy for Grönwall-type constraints is constructed and it is proved that it is the optimal strategy of the pursuer. In addition, the optimal strategy of the evader is constructed and the optimal pursuit time is obtained. The concept of a parallel pursuit strategy (Π-strategy for short) was introduced and used to solve the quality problem for "life-line" games by L.A.Petrosjan. This work develops and expands the works of Isaacs, Petrosjan, Pshenichnyi, and other researchers, including the authors.The present research was partially supported by the National Fundamental Research Grant Scheme FRGS of Malaysia (Project No.01-01-17-1921FR) and by the National Fundamental Research Grant Scheme of the National University Uzbekistan (Project No.FR-GS-33)
A decomposition technique for pursuit evasion games with many pursuers
Here we present a decomposition technique for a class of differential games.
The technique consists in a decomposition of the target set which produces, for
geometrical reasons, a decomposition in the dimensionality of the problem.
Using some elements of Hamilton-Jacobi equations theory, we find a relation
between the regularity of the solution and the possibility to decompose the
problem. We use this technique to solve a pursuit evasion game with multiple
agents
A formulation and analysis of combat games
Combat is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives. With each opponent is associated a target in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously or in neither, a joint capture or a draw, respectively, is said to occur. Resolution of the encounter is formulated as a combat game; namely, as a pair of competing event-constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero-sum differential game. Otherwise the optimal strategies are computed from a resulting non-zero-sum game. Since optimal combat strategies frequencies may not exist, approximate of delta-combat games are also formulated leading to approximate or delta-optimal strategies. To illustrate combat games, an example, called the turret game, is considered. This game may be thought of as a highly simplified model of air combat, yet it is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit-evasion games
A formulation and analysis of combat games
Combat which is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives is outlined. A target set is associated with each opponent in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously, or in neither, a joint capture or a draw, respectively, occurs. Resolution of the encounter is formulated as a combat game; as a pair of competing event constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero sum differential game. Otherwise the optimal strategies are computed from a resulting nonzero sum game. Since optimal combat strategies may frequently not exist, approximate or delta combat games are also formulated leading to approximate or delta optimal strategies. The turret game is used to illustrate combat games. This game is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit evasion games
Decomposition of Differential Games
This paper provides a decomposition technique for the purpose of simplifying
the solution of certain zero-sum differential games. The games considered
terminate when the state reaches a target, which can be expressed as the union
of a collection of target subsets; the decomposition consists of replacing the
original target by each of the target subsets. The value of the original game
is then obtained as the lower envelope of the values of the collection of games
resulting from the decomposition, which can be much easier to solve than the
original game. Criteria are given for the validity of the decomposition. The
paper includes examples, illustrating the application of the technique to
pursuit/evasion games, where the decomposition arises from considering the
interaction of individual pursuer/evader pairs.Comment: 10 pages, 2 figure
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