Hammerstein model identification of multivariable nonlinear systems in the presence of colored noises

Nonlinear multi-input multi-output (MIMO) models seem quite suitable to represent most industrial systems and many control problems. Besides, the outputs of the real systems are usually correlated with noises which might not satisfy the assumption of white noises. This paper proposes an efficient identification method for a class of nonlinear MIMO systems in the presence of colored noises. For this purpose, the multivariable Hammerstein model is considered which consists of a static multivariable nonlinearity followed by a dynamic multivariable linear system. The nonlinear part of the multivariable Hammerstein model is approximated based on arbitrary vector-based basis functions, and the linear part is modeled by an ARMAX/CARMA like model. Due to the multivariable nature of the system, the proposed model includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. Here, the hierarchical least squares iterative (HLSI) algorithm is used to approximate the unknown parameters as well as the noises. As the results show, this approach is quite efficient for identification of nonlinear colored MIMO systems.