Iterative Identification of Hammerstein Parameter Varying Systems With Parameter Uncertainties Based on the Variational Bayesian Approach

The identification of the multiple model-based Hammerstein parameter varying systems is studied in this paper. The parameters of the considered systems vary as the systems perform on different operating conditions. For each local model, the input nonlinear output-error structure is introduced to describe the dynamical property. Allocating an exponential weighting function to each local model, the nonlinear dynamics of the global system is approximated by combining all local models. The variational Bayesian (VB) approach is adopted to find the solution to the problem of parameter estimation. For the parameter uncertainties, instead of the point estimation, the posterior distribution of each model parameters is obtained under the framework of the VB approach. Two numerical simulation examples and an experiment carried on a multitank system have been employed to demonstrate that the proposed approach can work effectively.