A New On-line Structure Selection Algorithm for MIMO State Space Models

Abstract

MIMO linear system identification is usually developed in a canonical form It has been pointed out that sometimes there exist some numerical problem concerning system identification because of its uniqueness. The overlapping structure model is suggested in 1974, since then, several structure selection algorithms have been developed.A new on-line structure selection algorithm for MIMO linear systems is described in this paper. It uses the average diagonal elements of the inverse of the information latrix (EVN) as measure of the conditoning of parametrization. According to the concept of the relative correlativity, the most independent vectors are seccessively selected from the Hankel matrix of the system with a modified Gram-Schmidt orthogonalization method. The structure of the better conditioning of the parametrization is thus obtained. The relation of overlapping parametrization between state space and the I/O difference equation models is derived, so that the realization of overlapping parametrization of state space form can be obtained by simple elementary operations. Combining any recursive algorithm for parameter estimation (e.g. RLS, RIV, RGLS etc.) with the algorithm of structure selection in this paper, on-line algorithm for overlapping state space model is readily developed.Computer simulation results show the applicability of the above algorithm.