Auxiliary Model-based Stochastic Gradient Algorithm for Multivariable Output Error Systems

The identification problem of multivariable output error systems is considered in this paper. By constructing an auxiliary model using available input-output data and by replacing the unknown inner variables in the information vector with the outputs of the auxiliary model, an auxiliary model-based stochastic gradient (AM-SG) identification algorithm is presented. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates given by the AM-SG algorithm converge to their true values. The AM-SG algorithm with a forgetting factor is given to improve its convergence rate. The simulation results confirm the theoretical findings.