Identification of non-linear systems by recursive kernel regression estimates

Abstract Identification of non-linear, dynamical systems described by the Hammerstein model are discussed. Such a system consists of a multi-input single-output nonlinear, memoryless subsystem followed by a dynamic, linear subsystem. Outputs of both subsystems are corrupted by random noise. The parameters of the linear subsystem are identified by a correlation technique. The main contribution lies in estimating the non-linear, memoryless subsystem. The identification algorithm is based on the recursive kernel regression estimate. No restrictions are imposed on the functional form of the non-linearity as well on its continuity. We prove global convergence of the algorithm regardless of the distribution of the random input and for outputs with bounded moment of order greater than 2. The rate of convergence is obtained for the Lipschitz non-linearities and all input distributions.

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