Gradient-Based Identification Methods for Hammerstein Nonlinear ARMAX Models |
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| Authors: | Feng Ding Yang Shi Tongwen Chen |
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| Institution: | (1) Control Science and Engineering Research Center, Southern Yangtze University, Wuxi, 214122, China;(2) Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, Canada, S7N 5A9;(3) Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada, T6G 2V4 |
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| Abstract: | 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.
An erratum to this article is available at . |
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| Keywords: | convergence properties Hammerstein models least squares martingale convergence theorem parameter estimation recursive identification stochastic gradient Wiener models |
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