Identification of nonlinear MIMO block-oriented systems with moving average noises using gradient based and least squares based iterative algorithms

Nonlinear Multi-Input Multi-Output (MIMO) models seem quite suitable to represent most industrial systems and many control problems. Furthermore, the outputs of the real systems are usually corrupted with noises which might not satisfy the assumption of white noises. This paper presents simple and efficient identification methods for nonlinear MIMO systems in the presence of colored noises. In the proposed approaches, three classes of MIMO block-oriented structures including Hammerstein, Wiener, and Hammerstein–Wiener models are studied. Appropriate and flexible representations of these models lead to a pseudo-linear-in-the-parameter problem that contains some terms related to the colored noises which are not known a priori. In this paper, gradient based and least squares based iterative learning algorithms are invoked which can successfully estimate the matrix of unknown parameters as well as the colored noises. The efficiency of the proposed identification schemes is investigated through two simulated and a real process as case studies. As the results show, these approaches are quite efficient for identification of nonlinear colored MIMO systems.