Distributed Parameter Differential Games and Sensitivity Synthesis of Optimal Strategies

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Distributed parameter differential games and sensitivity synthesis of optimal strategies for a game with terminal constraints are discussed in this paper.In the first part of the paper, minimax problems are analyzed for functionals defined on real Hilbert spaces, where an existence theorem for saddle points is derived. As applications of the above theory, distributed parameter differential games with distributed controls, boundary controls or pointwise controls are considered. In each case, the necessary and sufficient conditions for existence of saddle points are derived in the form of variational inequalities.Secondly the game with terminal constraints is investigated, where the playability property plays an important role. The sensitivity synthesis of optimal strategies for the problem is developed to make up for the undesirable effects caused by the system parameter variations. In this sensitivity game, the central role is played by the combined system, which consists of a model equation and its parameter sensitivity equation. To ensure the existence of optimal strategies, the playability property of the combined system is examined. By giving simple examples, the effectiveness of the present sensitivity synthesis is illustrated.
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