The functioning of real economic processes is always carried out in conditions of uncer tainty and under influence of random factors.In this connection there is a necessity for adaptive control systems use. To get maxi mum profit is, in fact, a goal of the real eco nomic process control.In the present paper the task of adaptive control systems synthesis is examined at the given status tracking, which corresponds to the maximum profit of the existing market.Let mathematical model of the object func tioning be described by a system of the linear non-stationary stochastic differential equa tions of a kind: x(t) = A(t)x(t)+ B(I)u(l) + F(I)q(I), x(IO)where x(t) -na dimensional condition vec tor, u(t) -mdimensional vector of a con trol, q(t) -II -dimensional vector of accidental disturbances which is considered to be a Gaussian noise with the following per formances:A(t), B(t), F(t) -dynamic matrixes of the appropriate dimensions.Let's consider, that the model of object contains unknown parameters, which form N dimensional vector e. Thus , a status and parameters vector has a Gaussian distribu tion, Le.