Dynamic optimization problems 55 (2.13), are A n = x n i and A n = t n n f 0 - t n s i=1 n f 0 n - x i s i=1 P n-1 f i n n x n-1 x i i  n + P n-1 x n-1 i - P n = 0 x n i (2.24) P n-1 f i n x n-1 t n i  n + P n P n-1 - n = 0 t t n-1 (2.25) They are complemented by the stationarity conditions for the controls  n A n n = f 0 -  n s j=1 P n-1 x j f n - n-1 j P n-1 = 0 t n-1 (2.26) and the maximum condition for A n with respect to u n expressed in a special form P n-1 n s P n-1 n