Identification of Regularized Models in the Linear Regression Class

The problem of identification of complex discrete systems in the class of linear regression models is considered. The problem of identifying an exact model on noisy initial data is known to be ill-posed. Under limited uncertainty of initial data, it is proposed to find an approximate regularized solution and use model’s dimension as a regularization parameter. Two techniques for estimating the dimension of the model have been developed and investigated. They make it possible to find an approximate solution to the identification problem, consistent in accuracy with the data error. On the basis of numerical modeling, the developed identification methods have been analyzed and their efficiency has been evaluated.