A Kiefer‐Wolfowitz Algorithm Based Iterative Learning Control for Hammerstein‐Wiener Systems

The iterative learning control (ILC) is considered for the Hammerstein-Wiener (HW) system, which is a cascading system consisting of a static nonlinearity followed by a linear stochastic system and then a static nonlinearity. Except the structure, the system is unknown, but the system output is observed with additive noise. Both the linear and nonlinear parts of the system may be time-varying. The optimal control sequence under the tracking performance is first characterized, which, is however, unavailable since the system is unknown. By using the observations on system output the ILC is generated by a Kiefer-Wolfowitz (KW) algorithm with randomized differences, which aims at minimizing the tracking error. It is proved that ILC converges to the optimal one with probability one and the resulting tracking error tends to its minimal value. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

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