Two-person game with nash equilibrium in optimal control problems |
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Authors: | Anatoly Antipin |
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Institution: | 1. Computing Center of Russian Academy of Sciences, Vavilov str., 40, 119333, Moscow, Russia
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Abstract: | A two-person game with a Nash equilibrium is formulated for optimal control problems with a free right end and a linear differential system. The game is reduced to the calculation of a fixed point of an extremal mapping, which in turn is reduced to a variational inequality with linear constraints generated by systems of linear differential controllable processes. An extra-gradient iterative method is proposed for calculating the Nash equilibrium of the dynamic game. The convergence of the method is proved. |
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