On a class of nonzero-sum,linear-quadratic differential games |
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Authors: | M H Foley W E Schmitendorf |
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Institution: | (1) Department of Mechanical Engineering and Astronautical Sciences, Northwestern University, Evanston, Illinois |
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Abstract: | A class of two-player, nonzero-sum, linear-quadratic differential games is investigated for Nash equilibrium solutions when both players use closed-loop control and when one or both of the players are required to use open-loop control. For three formulations of the game, necessary and sufficient conditions are obtained for a particular strategy set to be a Nash equilibrium strategy set. For a fourth formulation of the game, where both players use open-loop control, necessary and sufficient conditions for the existence of a Nash equilibrium strategy set are developed. Several examples are presented in order to illustrate the differences between this class of differential games and its zero-sum analog.This research was supported by the National Science Foundation under Grant No. GK-3341. |
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