The present paper deals with a finite-time differential game of m players with nonzero sum. It should be emphasized that the players’ states are governed by boundary value ODE systems (rather than initial value systems). By the end of the game we understand an equilibrium situation, which is attained by applying an equlibrium control strategy. So our purpose is to design a well-founded suitable algorithm for equilibrium control search. In order to fulfil this task we shall make use of optimal control techniques.

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