Hierarchical multi-innovation extended stochastic gradient algorithms for input nonlinear multivariable OEMA systems by the key-term separation principle

This paper focuses on the identification of input nonlinear multivariable systems (i.e., Hammerstein multi-input multi-output nonlinear systems) described by output-error moving average models. Based on the key-term separation principle, we separate a proper key term in the nonlinear system and transform a complex nonlinear optimization problem into a pseudo-linear optimization problem which does not involve the products of the parameters between the linear parts and the nonlinear parts. Thus, a hierarchical extended stochastic gradient (H-ESG) algorithm is given and a hierarchical multi-innovation extended stochastic gradient (H-MI-ESG) algorithm is derived for the nonlinear systems. The proposed H-MI-ESG algorithm is an extension of the H-ESG algorithms. Compared with the over-parameterization-based least-squares identification algorithm, the H-ESG and H-MI-ESG algorithms have high computational efficiency. The simulation results show the effectiveness of the proposed algorithms.

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