On nonparametric identification of cascade nonlinear systems

Systems consisting of linear dynamic and memoryless nonlinear elements are identified. This includes the Hammerstein and Wiener cascade models. The input signal is the Gaussian stochastic process. The goal is to recover the system nonlinearity from input-output observations, signals interconnecting the elements are not measured. This is resolved by relating the posed identification problem to the theory of linear integral equations. Deconvolution procedures for recovering the nonlinearities are proposed using orthogonal series techniques. Conditions for global convergence of the established estimates are provided. The rate of convergence is also evaluated