Identification of Hammerstein systems with continuous nonlinearity

•We use the Weierstrass approximation theorem to simplify the model of the Hammerstein system.•We propose an M-SG algorithm to increase the convergence rate of the SG algorithm.•When the convergence index is getting smaller, the convergence rate of the M-SG algorithm is getting faster.•Compared with the SG algorithm and the M-SG algorithm, the PSO algorithm can increase the estimation accuracy.

This paper deals with the parameter identification problem for a Hammerstein system with continuous nonlinearity. Taking into account the unknown structure of the continuous nonlinearity, the Weierstrass approximation theorem is introduced to simplify the nonlinearity. Then a stochastic gradient algorithm and a particle swarm optimization algorithm are proposed to estimate all the unknown parameters of the Hammerstein system. The applicability of the approaches is illustrated by a simulation example.