R. Isaacs. Dierential Games. Wiley, New York, NY, 1965.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....using the Extender Kalman Filter. The main problem with these map building techniques is that they are time consuming and computationally expensive, even in the case of simple two dimensional rectilinear environments [2] On the other hand, most of the literature in pursuit evasion games, see e.g. [3], 4] 5] 6] 7] assumes worst case motion for the evaders and an accurate map of the environment. In practice, this results in overly conservative pursuit policies applied to inaccurate maps built from noisy measurements. In [8] the pursuit evasion game and map building problems are ....

R. Isaacs, Di#erential Games, John Wiley & Sons, 1965.

....the set (solution, Wiener process, control) does not depend on the probability space. Thus, either way, the sup u22U2 is well de ned for each rule for player 1. As 0, the inf sup is monotonically decreasing, since player 1 can make decisions more often. Similar monotonicity was discussed in [20]. The analogous comments hold for (2.8) In Section 4, it will be seen that the infs and sups could be taken over the relaxed controls without changing the results. Under our conditions, Theorem 5.1 says that there is a saddle point in that V (x) V (x) V (x) for all x 2 G: 2:9) The use ....

....and sups could be taken over the relaxed controls without changing the results. Under our conditions, Theorem 5. 1 says that there is a saddle point in that V (x) V (x) V (x) for all x 2 G: 2:9) The use of limits of discrete strategies to de ne the upper and lower values goes back to [16, 17, 20], where discrete time games were used to approximate continuous time games. The Elliott Kalton de nition [13] does not require discretization and admits the widest class of strategies to date. But, various approaches based on discretized strategies are shown to yield the same values as those given ....

A. Friedman. Dierential Games. Wiley, New York, 1971.

....programs and pictures of views produced by them are shown. Key words. scienti c visualization, di erential games, value function, singular surfaces, OpenGL, ARCBALL controller AMS subject classi cations. 68U05, 90D25, 49N55 1. Introduction. Dynamics of a di erential game is usually described [1, 2, 3] as x = F (t; x; u; v) Here t is the time, x is the phase vector (possibly, multidimensional) u and v are the controls of the rst and second players. These controls are taken from compacta P and Q, correspondingly. The case is quite typical when the terminal time T is xed and the payo ....

....is quite typical when the terminal time T is xed and the payo function (x) is determined at the terminal instant. The rst player manages his control to minimize the payo , the second one maximizes it. The players controls are of the feedback type. For the accurate de nitions, one can see [1, 2, 3]. For a quite wide class of games, the best guaranteed results of players are equal. Corresponding common function (t; x) 7 V (t; x) is called the value function of the game. The construction of the value function is the essential part of solving a di erential game. There are a number of ways ....

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R.Isaacs, Dierential games, John Wiley and Sons, New York, 1965.

....of the value function of the homicidal chau eur di erential game are given. Key words. di erential games, value function, numerical methods, scienti c visualization AMS subject classi cations. 49N55, 90D25, 90D26, 68U05 1. Introduction. Typical problems in the theory of di erential games [7] [9] are those with the payo be the time of attaining a given terminal set M: The rst player minimizes the attaining time but the second player maximizes it. If the game has a stationary dynamics, the value function V is a function of the state vector x and does not depend on the time t: The ....

....x 0 is de ned as the shortest time that the rst player can guarantee using feedback controls. Similarly, the best guaranteed result of the second player is de ned as the longest time that the second player can guarantee using feedback controls. The best guaranteed results of the players coincide [7] [9] for a wide class of di erential games. The common value is called the meaning of the value function for the state x 0 . On the whole, the function x V (x) is considered. The computation of the value function is one of the most important steps in solving di erential games. As an example of ....

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R. Isaacs, Dierential games, New York, John Wiley, 1965.

....expected cost criteria to be optimized. Limit results like (1.10) can be proved by viscosity solution methods, applied to the corresponding nonlinear PDEs. See [FM1] Ja] and also in a special case Section 3.3. 3.2 Di erential games. The theory of two player di erential games began with R. Isaacs [I]. Let us consider the following class of di erential games, on a nite horizon 0 t T . For notational simplicity, we assume that the game state x t 2 IR 1 is one dimensional. The maximizing controller (or player) chooses u t 2 U and the minimizing controller chooses v t 2 IR 1 . The state ....

R. Isaacs, Dierential Games, Wiley, New York, 1965.

....game. There are well known diculties in making this intuitive formulation precise. To avoid these diculties, various rigorous de nitions of lower di erential game have been made (using time discretizations, Elliott Kalton strategies etc) See Elliott and Kalton [EK] Fleming 23 [F 1] Friedman [Fr]. Any reasonable de nition provides a lower game value W = W (x; T ) which satis es in the viscosity sense the Isaacs PDE (2:5) W T = max u min v (f(x; u) g(x; u)v) W x L(x; u) 1 2 v 2 # (2:6) W (x; 0) G(x) A uniqueness theorem for viscosity solutions to (2.5) 2.6) ....

A. Friedman, Dierential Games, Wiley, New York, 1971.

....1 i I: But noting (22) and (2b) the above inequality becomes an equality. Remark: The fact that the min max operations commute in some order, for some information patterns, was rst pointed out and utilized by Witsenhausen [2] in the context of deterministic sampled linear systems. Friedman [3] and Bertsekas and Rhodes [4] also used this commutativity property in the context of zero sum di erential games and minimax control of uncertain plants, again for deterministic systems and for some special information patterns. 4 Concluding Remarks The treatment here can be generalized in a ....

A. Friedman, Dierential games, Wiley, New York, (1971).

....a two stage process: rst, a map of the region is built and then, the pursuit evasion game takes place on the region that is now well known. In fact, there is a large body of literature on any of these topics in isolation. On pursuit evasion games the reader is referred to the classical reference [1] or the more recent textbook [2] For a formulation of this type of games that takes visual occlusion into account, see [3, 4] On map building, see, e.g. 5, 6] and references therein. Search and rescue problems [7, 8] are also closely related to the pursuit evasion games addressed here. In ....

R. Isaacs, Dierential Games. New York: John Wiley & Sons, 1965.

....have been considered in dynamic game theory, graph theory, computational geometry, and robotics. In game theory, pursuit evasion scenarios, such as the Homicidal Chau eur problem, express di erential motion models for two opponents, and con ditions of capture or optimal strategies are sought [5]. In graph theory, several interesting results have been obtained for pursuit evasion in a graph, in which the pursuers and evader can move from vertex to vertex until eventually a pursuer and evader lie in the same vertex [1, 6, 10, 11, 12, 13] The pursuer evasion problem using a single ....

R. Isaacs. Dierential Games. Wiley, New York, 1965.

....have been considered in dynamic game theory, graph theory, computational geometry, and robotics. In game theory, pursuit evasion scenarios, such as the Homicidal Chau eur problem, express di erential motion models for two opponents, and conditions of capture or optimal strategies are sought [5]. In graph theory, several interesting results have been obtained for pursuit evasion in a graph, in which the pursuers and evader can move from vertex to vertex until eventually a pursuer and evader lie in the same vertex [1, 6, 10, 11, 12, 13] The pursuer evasion problem using a single ....

R. Isaacs. Dierential Games. Wiley, New York, NY, 1965.

....converge to the adjoint of x( 1650 PIERRE CARDALIAGUET 2.3. Barrier solutions and the Pontryagin principle. We now prove that, under some assumptions of di#erentiability of the hamiltonian H, barrier solutions satisfy the Pontryagin principle. In Isaacs pioneering work on di#erential games [18], semipermeable hypersurfaces are constructed by using the method of characteristics, which is very close to the Pontryagin principle. We show here that this method of construction is a priori justified since the barrier solutions indeed satisfy the Pontryagin principle. THEOREM 2.2. Assume that ....

R. ISAACS, Di#erential Games, John Wiley, New York, 1965.

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R. Isaacs. Dierential Games. Wiley, New York, NY, 1965.

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R. Isaccs. Di#erential Games. Wiley, New York,NY, 1975.

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R. Isaacs. Di#erential Games. Wiley, New York, NY, 1965.

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R. Isaacs. Di#erential Games. Wiley, 1965.

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Lewin, J., Di#erential Games, Springer, 1994.

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Isaacs R., Di#erential games, John Wiley & Sons, Inc., New York, 1965.

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