Multivariable Frequency Domain Identification via 2-Norm Minimization

This paper develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. In order to improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a MIMO plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.