Linear Stochastic Differential Games
HARVARD UNIV CAMBRIDGE MA CAMBRIDGE
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The solution for a class of stochastic pursuit-evasion differential games between two dynamic systems is given this class includes those games where one of the players has perfect knowledge of the state of the game while the other player is constrained to make noisy measurements on this state. The dynamic systems involved are linear and the performance index which is optimized is quadratic. The strategy for the player with perfect information is not always a realizable one. It is shown that this player can implement this strategy, however, if the number of his control variables is as great as the number of the state variables involved in the pursuit and evasion. Thus the solution obtained is applicable for the classical interception game in euclidean space. Several aspects of this game are studied in detail. The asymmetric roles of the pursuer and evader are discussed in general and relationships drawn between the deterministic and stochastic cases. It is pointed out that this game requires -- in reality -- the solution to a non zero-sum game since the two different information sets employed by the two players cause each player to evaluate the criterion differently. The certainty-equivalence principle which characterizes the standard stochastic control problem is shown to be applicable to this class of differential games. Examples of the classical interception game are given and numerical results presented.
- Operations Research