On asymptotic properties of real-time identification algorithms based on dynamic stochastic approximation

The algorithms of dynamic stochastic approximation type are proposed for real-time identification of multivariable linear dynamic discrete-time systems with stochastic parameters. These algorithms can be considered as the general representatives of a class of gradient-type equation-error recursive identification methods. The analysis of their asymptotic properties is presented. It is proved that the algorithms converge either in the mean-square sense, or in the sense of keeping the mean-square error bounded, depending on system parameter properties. Convergence conditions are expressed in terms of inherent system characteristics, e.g., properties of the impulse response matrices and their realizations. A large class of input random processes is supposed.