Parameter Estimation for Multivariable Hammerstein Systems Based on the Decomposition Technique

The focus of this paper is the parameter identification of multivariable Hammerstein controlled autoregressive moving average (for short, CARMA) systems. Based on the internal relationship between the nonlinear submodel and linear subsystem, the multivariable nonlinear CARMA systems are converted into a special identification model which includes the bilinear parameter vector and the other parameter vector. In order to address the above bilinear parameter vector, we construct two the corresponding estimation models in which each identification model is linear to the corresponding parameter vector by using matrix transformation, and developed an adaptive estimation approach to interactively identify the parameter vectors through the usage of the hierarchical identification principle and filtering technique. The conditions of convergence are discussed through the usage of the martingale theorem. The comparative simulation results show that the presented approach produces higher estimation accuracy and faster convergence rate than some publishing identification methods.