Nonparametric models of the Hammerstein dynamical objects

The problem of nonlinear dynamical systems of the Hammerstein type identification is considered. Systems in the conditions of partial parameterization are considered. In this case structure and parameters of equation, which describe the linear dynamical part of the object, are unknown. The common type of nonlinearity is assumed to be known with the set of parameters. It is required to construct the mathematical model of the investigation system, which is based on the input-output measures sample. The proposed method of dynamic objects modeling is based on the nonparametric estimation of linear and nonlinear parts of the system. At first it is offered to estimate the nonlinear element parameters, and to the input of system consistently applied different input actions. Then the linear dynamical part model can be constructed as a Duhamel integral, where the impulse response function is estimated with nonparametric algorithm. Presented algorithm doesn’t require a complete priory information about the object structure. In the work the results of computer modeling of the Hammerstein type systems with the quard and the saturation nonlinearity are shown. This nonparametric model can describe the investigation systems with different types of nonlinearity, in conditions of noise in the measure channels, and with different sample sizes and input actions. The numerical researches show that the algorithms should be used to identify the Hammerstein type nonlinear systems.