Identification of Wiener systems based on fixed point theory

In this paper, we propose a new method for the identification of Wiener systems based on fixed point theory. The linear part of the system is an infinite impulse response (IIR) system and the nonlinear static function is allowed to be non-continuous or non-smooth. Our proposed technique transforms the estimation of parameters to finding a fixed point of a nonlinear equation. We show the existence of the fixed point and also develop an iterative algorithm to find the fixed point. It is proved that, the determined fixed point is actually a global minimum point of the cost function and it is unique, and thus global convergence of the estimates is ensured. The performance of the proposed approach is illustrated by simulation studies.