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

Liu, Yanjun; Sheng, Jie; Ding, Ruifeng

Comput. Math. Appl. 59, No. 8, 2615-2627 (2010).

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

Keywords:

recursive identification; parameter estimation; multivariable systems; stochastic gradient; convergence properties

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