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  • Articles  (18)
  • Differential games  (18)
  • 2020-2022
  • 1975-1979  (18)
  • 1950-1954
  • Mathematics  (18)
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  • Geosciences
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  • Mathematics  (18)
  • History
  • Geosciences
  • 1
    Electronic Resource
    Electronic Resource
    The effect of playability in differential games on the relation between best guaranteed costs and saddlepoint values (1975)
    Springer
    Journal of optimization theory and applications 15 (1975), S. 509-516 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; saddlepoint value ; guaranteed cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a classical two-person zero-sum game, the decision pairs are members of a product space of admissible decision sets. Such a game possesses a number of desirable properties. In a differential game in which termination is required and a playability requirement is imposed on decision pairs, some properties of classical games need not hold. This is demonstrated by means of an example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933742
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  • 2
    Electronic Resource
    Electronic Resource
    Feedback strategies with finite memory in differential games (1979)
    Springer
    Journal of optimization theory and applications 27 (1979), S. 127-134 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; closed-loop controls ; feedback control ; strategy ; information delays
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown that, in differential games, strategies can be defined for the players in such a way that their controls depend, for each timet, on a finite section of the past of the trajectoryx(t). In particular,s-delay,r-memory strategies can be defined as in the Varaiya-Lin approach. It is shown that, for deterministic differential games with terminal payoff, the upper and lower values of the game so defined, are independent of the lengthr of the memory. Lettingr → 0, a feedback strategy is obtained which depends only on the present (and infinitesimal past) of the trajectoryx(t).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933330
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  • 3
    Electronic Resource
    Electronic Resource
    A differential game of incomplete information (1979)
    Springer
    Journal of optimization theory and applications 28 (1979), S. 213-232 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; incomplete information ; homing problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we study a differential game of incomplete information. In such a game, the cost function depends on parameter ϑ. At the start of the game, only one of the players knows the value of this parameter, while the other player has only a (subjective) probability distribution for the parameter. We obtain explicit expressions for both the value of the game and the two players' optimal strategies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933243
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  • 4
    Electronic Resource
    Electronic Resource
    Unique winning policies for linear differential pursuit games (1979)
    Springer
    Journal of optimization theory and applications 29 (1979), S. 629-658 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit-evasion problems ; optimal strategies ; control theory ; duality theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study optimal control problems which are the duals, in a specified sense, to a certain class of linear differential games. Directly verifiable conditions, in terms of the data of the game, for uniqueness of solutions of the dual problem and thus for uniqueness of winning policies for the differential game, are derived. As a byproduct, in the particular context of two-dimensional problems, a strong result concerning normality is obtained. As a second byproduct, several geometrical and topological properties of thestar difference are derived. This set operation is of paramount importance for the study of rich classes of differential and difference games extending far beyond that treated here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934455
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  • 5
    Electronic Resource
    Electronic Resource
    A class of linear evasion problems (1975)
    Springer
    Journal of optimization theory and applications 16 (1975), S. 147-164 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit-evasion problems ; min-max functions ; directional differentiability ; sequential upper-semicontinuity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A special class of linear evasion problems is discussed. It turns out that the evasion problems are more difficult than pursuit problems in that evader has to prevent capture on an infinite interval of time. Some of the basic facts and difficulties inherent to evasion problems are pointed out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935629
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  • 6
    Electronic Resource
    Electronic Resource
    On a class of linear differential games (1975)
    Springer
    Journal of optimization theory and applications 17 (1975), S. 511-522 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit-evasion ; stability ; uncertain systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Saddlepoint strategies are deduced for a class of linear, single-input differential games. Conditions necessary for a saddle-point, as well as sufficient conditions, are discussed. The results are illustrated with a simple example. For the case of one control subject to a norm bound and the other to a quadratic penalty, the results are extended to the vector case and applied to the stabilization of a system subject to norm-bounded input disturbance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932787
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  • 7
    Electronic Resource
    Electronic Resource
    A sufficiency condition for coalitive pareto-optimal solutions (1976)
    Springer
    Journal of optimization theory and applications 18 (1976), S. 93-102 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; Pareto optimality ; multicriteria optimization ; games with coalitions ; cooperative games
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In ak-player, nonzero-sum differential game, there exists the possibility that a group of players will form a coalition and work together. If allk players form the coalition, the criterion usually chosen is Pareto optimality whereas, if the coalition consists of only one player, a minmax or Nash equilibrium solution is sought. In this paper, games with coalitions of more than one but less thank players are considered. Coalitive Pareto optimality is chosen as the criterion. Sufficient conditions are presented for coalitive Pareto-optimal solutions, and the results are illustrated with an example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933797
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  • 8
    Electronic Resource
    Electronic Resource
    On saddle-point optimality in differential games (1976)
    Springer
    Journal of optimization theory and applications 18 (1976), S. 141-151 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; playability ; saddle-point optimality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A family of two-person, zero-sum differential games in which the admissible strategies are Borel measurable is defined, and two types of saddle-point conditions are introduced as optimality criteria. In one, saddle-point candidates are compared at each point of the state space with all playable pairs at that point; and, in the other, they are compared only with strategy pairs playable on the entire state space. As a theorem, these two types of optimality are shown to be equivalent for the defined family of games. Also, it is shown that a certain closure property is sufficient for this equivalence. A game having admissible strategies everywhere constant, in which the two types of saddle-point candidates are not equivalent, is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933800
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  • 9
    Electronic Resource
    Electronic Resource
    A differential game without a qualitative saddle point (1976)
    Springer
    Journal of optimization theory and applications 20 (1976), S. 251-254 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; game theory ; stability analysis ; qualitative saddle points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Saddle points are defined for two-person differential games in which the players have opposing preference orderings over lotteries on a set of qualitative objectives, rather than numerical payoff functions. A simple example is then given of a game without such a qualitative saddle point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01767455
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  • 10
    Electronic Resource
    Electronic Resource
    Iterative techniques for Riccati game equations (1977)
    Springer
    Journal of optimization theory and applications 22 (1977), S. 51-61 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; dynamic programming ; Riccati equation ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present a monotone iterative technique for the computation of a solution of a Riccati-type equation relevant to the theory of differential games. For this purpose, we show that the Kleinman algorithm for Riccati equation computations converges under extremely general conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00936720
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