Asymptotical estimates of maximal likelihood for parameters of a closed-loop stochastic system

The paper is concerned with identification of a linear closed-loop system with constant parameters and subjected to unobservable Gaussian noises correlated in time. The method of maximal likelihood is used for solution. Sufficient conditions are obtained for convergence almost certainly of estimates of maximal likelihood for parameters of a closed-loop system to the true values with increase in the size of the sample. The notions of structural nonidentifiability of the plant and the feedback are introduced. For closed-loop systems with noises in the plant and the feedback conditions for structural nonidentifiability of the feedback are given. For closed-loop system without noise in the feedback the reason for structural nonidentifiability of the plant is uncovered and methods for its elimination studied.