Stochastic approximation in nonparametric identification of Hammerstein systems

Derived from the idea of stochastic approximation, recursive algorithms to identify a Hammerstein system are presented. Two of them recover the characteristic of the nonlinear memoryless subsystem while the third one estimates the impulse response of the linear dynamic part. The a priori information about both subsystems is nonparametric. Consistency in quadratic mean is shown and the convergence rate is examined. Results of numerical simulation are also presented. Keywords– System identification, Hammerstein system, nonparametric identification, recursive identification, nonparametric regression, stochastic approximation.