Advanced Gauss Pseudospectral Method for Continuous-time Hammerstein System Identification

In the paper, an advanced Gauss pseudospectral method (AGPM) is proposed to estimate the parameters of the continuous-time (CT) Hammerstein model consisting of a CT linear block followed by a static nonlinearity. The basic idea of AGPM is to transcribe the CT identification problem into a discrete nonlinear programming problem (NLP), which can be solved with the well-developed sequential quadratic programming (SQP) algorithm. The nonlinear part of the Hammerstein system is approximated with the Gauss pseudospectral approximation method. The linear part is written as a controllable canonical form. AGPM can converge to the true values of the CT Hammerstein model with few interpolated Legendre-Gauss (LG) nodes. Lastly illustrative examples are proposed to verify the accuracy and efficiency of the method.