Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems.(English)Zbl 1193.60057

Summary: This paper studies the convergence of the stochastic gradient identification algorithm of multi-input multi-output ARX-like systems (i.e., multivariable ARX-like systems) by using the stochastic martingale theory. This ARX-like model contains a characteristic polynomial and differs from the conventional multivariable ARX system. The results indicate that the parameter estimation errors converge to zero under the persistent excitation conditions. The simulation results validate the proposed convergence theorem.

MSC:

 60G42 Martingales with discrete parameter 62L20 Stochastic approximation 93E10 Estimation and detection in stochastic control theory 62F12 Asymptotic properties of parametric estimators
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