Iterative Identification For A Class Of Wiener Nonlinear Systems

Wiener nonlinear systems are important branch of output error nonlinear systems,it consists of a linear dynamic subsystem followed by a static nonlinear block. Becauseof the complexity and diversity, using classical linear identifcation methods to identifynonlinear systems are generally have large errors. Iterative identifcation methods play akey role in system identifcation, and are widely used in parameter estimation. In thispaper, we derive a Newton iterative algorithm and a gradient iterative algorithm for aclass of Wiener nonlinear systems whose linear block are fnite impulse response modeland output error model. The proposed methods are very signifcant and have broadapplications. The results are described as follows.1. For the fnite impulse response model of linear block of Wiener nonlinear system-s(Wiener FIR nonlinear systems), the Newton iterative algorithm and the gradientiterative algorithm are proposed under the white noise and the colour noise. Basedon the hierarchical identifcation principle, the unmeasurable variables contained ininformation vectors can be replaced with their previous iterative estimates. Using thedecomposition technique, we identify the papameters of the linear part of the sys-tem as well as the nonlinear one respectively by means of Newton iterative algorithmand the gradient iterative algorithm. Finally, taking a Wiener nonlinear model as anexample, and the simulation results indicate that the proposed algorithm is efective.2. For the output error model of linear blocks of Wiener nonlinear systems, this paperderived the Newton iterative algorithm and the gradient iterative algorithm basedon the hierarchical identifcation principle. The simulation results indicate that theNewton iterative algorithm has faster convergence compared with that of the gradientiterative algorithm.In conclusion, in this paper, a Newton iterative identifcaton algorithm and a gradientiterative algorithm are proposed for a class of Wiener nonlinear systems, mainly involvedthe Wiener FIR nonlinear system and the Wiener output error nonlinear system, andfurther perform these algorithms by MATLAB. The simulations show that the proposedalgorithms are efective for the parameter identifcation of the Wiener nonlinear systems.At last, some difculties and problems and some further explore aspects in this feld areproposed, such as the convergence problem of the iterative algorithm.