Theory of differential games with integral payoff. Part II

Abstract

is g iven as the payoff of the game . H e r e x is the n v e c t o r of the p h a s e coo rd ina t e s of the con t ro l l ed objec ts ; the v e c t o r s u = {ui}, v = {vj} (i= 1 . . . . . r ; j = 1 . . . . . q) a r e the con t ro l l ing ac t ions (the s t r a t eg i e s ) of the f i r s t p l a y e r and s econd p l a ye r , reslSectively; t o and T a r e the f ixed ins tan t s of t ime at which the game T begins and ends; f Fdt and @ {x(T)) a r e ca l led the in teg ra l payoff and the t e r m i n a l payoff [1]. We a s s u m e