EXTRAPOLATION IN DISCRETE SYSTEMS WITH MULTIPLICATIVE PERTURBATIONS AT INCOMPLETE INFORMATION

The model with multiplicative perturbations and incomplete information is described by the equation: x(k + 1) = (A + Delta A)x(k) + (B + Delta B)u(k) + Sigma(m)(s=1)A(s)x(k)theta(s)(k) + f(k) + q(k), x(0) = x(0), where x(k) is an element of R-n is the state vector, u(k) is an element of R-p is the known input, f(k) is an unknown input; x(0) is a random vector (the covariance matrix N-0 = M{(x(0) - (x) over bar (0))(x(0) - (x) over bar (0))(T)} and the expectation (x) over bar (0) = M{x(0)} are assumed to be known); A, B, A(s) (s = 1...m) are known matrices; Delta A, Delta B are matrices of unknown parameters; q(k) and theta(s)(k) are Gaussian vector random sequences with the following characteristics: M{q(k)} = 0, M{q(k)q(T)(j)} = Q delta(kj), M{theta(s)(k)theta(T)(s)(j)} = Q delta(kj). The observation channel is described by the formula: y(k) = Sx(k) + v(k), where v(k) is a Gaussian random sequence with known characteristics. The problem solution is proposed to be performed on the basis of the separation principle using the optimal recurrent extrapolation, the least squares method with additional smoothing using the moving average algorithms and nonparametric estimators. It is shown that the use of smoothing algorithms for estimating an unknown input for a discrete model with multiplicative perturbations allows can improve the prediction accuracy.