Identification of a closed-loop stochastic system

Parametric identification of a linear feedback dynamic system containing noises in the planta and control unit is discussed. The method of maximum likelihood is used for the solution. The set of equations for plant and control unit parameter estimations is obtained. Asymptotic properties of parameter estimations are studied. Necessary, and sufficient conditions for convergence almost everywhere of estimations to true values are presented. It is shown that the maximum likelihood estimations of plant parameters computed without estimating control unit parameters, coverge to true values provided that plant is controllable.