Identification of a dynamical system with input nonlinearity

A novel identification approach based on an input-holding scheme is proposed for a class of nonlinear system which consists of a nonlinear element followed by a linear dynamical system. By only using an observed system output where the test input signal is held during a multiple of the output sampling interval, the parameters of the transfer function of the linear part can be identified first. Then the intermediate input between the nonlinear part and the linear part is reconstructed by using the estimated parameters of the linear part. Finally, the nonlinear element is identified by using the test signal and the reconstructed intermediate input. It is clarified that the consistency of the parameter estimates of the linear part is assured under some specified assumptions. The effectiveness of the proposed algorithm is examined in identification of a Hammerstein system which includes an unknown continuous and/or discontinuous nonlinearity such as a backlash.