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DISTRIBUTED PARAMETER DIFFERENTIAL GAMES.
WASHINGTON UNIV ST LOUIS MO DEPT OF SYSTEMS MECHANICAL AND AEROSPACE ENGINEERING
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The dissertation extends some of the results known for lumped parameter differential games to differential games which involve distributed systems. The distributed system is described by a linear second order partial differential equation with appropriate boundary conditions. Simultaneous distributed and boundary controls are considered and all performance criteria involved are quadratic. Two types of differential game are considered, the zero sum game and the nonzero sum game. The saddle point solution for the zero sum game is sought. For the nonzero sum game there are three types of solution which may be of interest. These are the Nash equilibrium, the noninferior, and the minimax. First the closed loop form of each of these solution types is found by using a dynamic programming appraoach. The partial differential equations which arise in the closed loop formulation are then solved using the normal modes method. Next, the open loop form of the various solution types mentioned above are sought. A variational calculus approach is used to find the necessary conditions for these types of solution. It is found that these open loop strategies are different than the closed loop strategies for the case of Nash strategies, but are the same as the closed loop strategies in the case of the noninferior, the minimax and the saddle point strategies. Author
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