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Gradient-based identification methods for Hammerstein nonlinear ARMAX models. (English) Zbl 1134.93321

Summary: Two identification algorithms, an iterative gradient and a recursive stochastic gradient based, are developed for a Hammerstein nonlinear ARMAX model, a linear dynamical block following a memoryless nonlinear block. The basic idea is to use the gradient search principle, to replace unmeasurable noise terms in the information vectors by their estimates, and to compute iteratively or recursively the noise estimates based on the obtained parameter estimates. Convergence analysis of the recursive stochastic gradient algorithm indicates that the parameter estimation error consistently converges to zero under certain conditions. The simulation results show the effectiveness of the proposed algorithms.

MSC:

93B30 System identification
93E03 Stochastic systems in control theory (general)
93C23 Control/observation systems governed by functional-differential equations
93E25 Computational methods in stochastic control (MSC2010)
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