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  • Articles  (14)
  • Differential games  (14)
  • Springer  (14)
  • American Chemical Society
  • American Geophysical Union (AGU)
  • Annual Reviews
  • 1980-1984  (14)
  • 1950-1954
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  • Mathematics  (14)
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  • Articles  (14)
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  • Springer  (14)
  • American Chemical Society
  • American Geophysical Union (AGU)
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  • Mathematics  (14)
  • 1
    Electronic Resource
    Electronic Resource
    Existence of value in differential games with terminal cost function (1983)
    Springer
    Journal of optimization theory and applications 39 (1983), S. 89-104 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; optimal strategies ; value of a game ; terminal cost function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A two-person, zero-sum differential game with general type phase constraints and terminal (not fixed) cost function is investigated. Player II (possessing complete information) can choose any strategy in the Varaiya-Lin sense, while his opponent (having incomplete information) can select any lower II-strategy introduced by Friedman (Ref. 1). The existence of a value and an optimal player II's strategy is obtained under assumptions ensuring that the sets of all admissible trajectories for the two players are compact in the Banach space of all continuous functions. The present paper largely extends the results of Ref. 2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934607
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  • 2
    Electronic Resource
    Electronic Resource
    Multimodel design of a Nash strategy (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 553-564 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; perturbation theory ; systems order reduction ; large-scale systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For interconnected systems with slow and fast modes, we analyze a multimodel design of a Nash equilibrium strategy. Decision makers use different models of the same system to obtain a composite strategy that approximates the exact Nash strategy. It is discussed in what sense this approximation holds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934477
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  • 3
    Electronic Resource
    Electronic Resource
    Remarks on capture-avoidance games (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 365-377 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit and evasion ; capture avoidance ; linear games
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We formulate the problems of capture and avoidance as differential games with terminal cost, thus avoiding some difficulties arising from choosing the terminal time or the closest distance as the cost. This puts capture and avoidance in the context of differential games, in the sense of Isaacs. The results are illustrated via linear differential games with hard control constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934558
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  • 4
    Electronic Resource
    Electronic Resource
    On qualitative differential games with two targets (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 587-598 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; first reachability of sets ; playability ; pursuit-evasion problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a qualitative differential game between two players, each with their own respective target. A player's objective is to steer the response of a dynamical system under the control of both players into his own target before his opponent can steer it to his. The sufficiency conditions given by Getz and Leitmann (Ref. 2), which ensure termination on a particular target, are improved. The theory is illustrated by a pursuit-evasion problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934645
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  • 5
    Electronic Resource
    Electronic Resource
    On a linear pursuit game with an unknown trap (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 421-445 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit games ; pursuit-evasion ; nonzero-sum games
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A linear pursuit game with a trap, the location of which is unknown to the evader, is defined and investigated. The cases in which one of the players has complete energy dominance over his adversary are solved completely. In the general case, when no player dominates, the solution is indicated for the two-stage game.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935325
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  • 6
    Electronic Resource
    Electronic Resource
    Generalization of the main equation of differential game theory (1984)
    Springer
    Journal of optimization theory and applications 43 (1984), S. 103-133 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; value function ; saddle points ; feedback strategy ; extremal strategy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider feedback, two-person, zero-sum differential games. We obtain two inequalities for the directional derivatives of the nonsmooth value function. We show that these inequalities, together with the boundary conditions, constitute necessary and sufficient conditions which the value function must satisfy. In the region where the value function is differentiable, the inequalities become the well-known main equation of differential game theory (Isaacs-Bellman equation). The results obtained here may be useful in the approximation of the value function by piecewise smooth splines and also in the classification of singular surfaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934749
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  • 7
    Electronic Resource
    Electronic Resource
    On the game of two cars (1984)
    Springer
    Journal of optimization theory and applications 44 (1984), S. 381-396 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit-evasion games ; piecewise programming strategy ; evasion strategy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Necessary and sufficient conditions for the existence of the evasion strategy in the so-called game of two cars are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935458
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  • 8
    Electronic Resource
    Electronic Resource
    On the isochronous and stroboscopic capture in differential games (1982)
    Springer
    Journal of optimization theory and applications 37 (1982), S. 115-119 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; isochronous capture ; stroboscopic strategy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Ref. 1, Hájek formulated the conjecture that isochronous capture is necessarily stroboscopic in linear differential games. Here, it is shown that this conjecture is not valid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934369
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  • 9
    Electronic Resource
    Electronic Resource
    A class of differential games for which the closed-loop and open-loop Nash equilibria coincide (1982)
    Springer
    Journal of optimization theory and applications 36 (1982), S. 253-262 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; Nash equilibria ; open-loop strategies ; closed-loop strategies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is well known that, in general, Nash equilibria in open-loop strategies do not coincide with those in closed-loop strategies. This note identifies a class of differential games in which the Nash equilibrium in closed-loop strategies is degenerate, in the sense that it depends on time only. Consequently, the closed-loop equilibrium is also an equilibrium in open-loop strategies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933832
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  • 10
    Electronic Resource
    Electronic Resource
    Two-target pursuit-evasion differential games in the plane (1981)
    Springer
    Journal of optimization theory and applications 34 (1981), S. 383-403 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit-evasion ; homicidal chauffeur ; Lyapunov methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two-target versions of the game of two cars and the homicidal chauffeur game are introduced. This enables us to consider pursuitevasion withouta priori role assignment. A generic example of the two-target homicidal chauffeur game is considered in detail; in particular, a map of the game and its corresponding winning strategies are found using Lyapunov methods of analysis. The effects of altering game parameters, such as the speed and maneuverability ratios, and the weapon system parameters are then presented. It is found that certain winning strategies include a swerve-type maneuver and that, for certain sets of parameters, regions of stagnation and different modes of draw occur.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934679
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  • 11
    Electronic Resource
    Electronic Resource
    Closed-loop Stackelberg solution to a multistage linear-quadratic game (1981)
    Springer
    Journal of optimization theory and applications 34 (1981), S. 485-501 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; multistage games ; Stackelberg strategy ; strategy with memory ; decentralized control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new solution of a two-person, nonzero-sum Stackelberg game, with linear dynamics, quadratic performance criteion, and closed-loop information available to both players, is presented. This solution is applicable to all problems where the leader is able to influence the objective function of the follower, and this function is strictly convex with respect to the control variable handled by the follower. The resulting equilibrium strategies adapt to the possible nonoptimal behavior of players at some stages of the game. The strategy of the leader has a simple interpretation of a threat formulated by the leader toward the follower and, if necessary, carried out one stage after the follower has played inconsistently with the leader's wishes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935889
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  • 12
    Electronic Resource
    Electronic Resource
    Singular differential game numerical techniques (1982)
    Springer
    Journal of optimization theory and applications 37 (1982), S. 69-87 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; singular arcs ; saddle points ; two-point boundary-value problems ; switching times ; closed-loop solutions ; inverse systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper develops a numerical technique to solve a class of zero-sum differential games with singular control. By using this technique and the application of inverse systems, a near-optimal closed-loop technique is developed to generate a numerical solution to this class of problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934367
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  • 13
    Electronic Resource
    Electronic Resource
    Remarks on capture-avoidance games (1982)
    Springer
    Journal of optimization theory and applications 37 (1982), S. 121-122 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit and evasion ; captureavoidance ; linear games
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Corrections to some results of Ref. 1 are stated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934370
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  • 14
    Electronic Resource
    Electronic Resource
    Existence of value in differential games with fixed time duration (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 581-598 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; optimal strategies ; value of a game
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A differential game of prescribed duration with general-type phase constraints is investigated. The existence of a value in the Varaiya-Lin sense and an optimal strategy for one of the players is obtained under assumptions ensuring that the sets of all admissible trajectories for the two players are compact in the Banach space of all continuous functions. These results are next widened on more general games, examined earlier by Varaiya.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934489
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