A methodology to enhance the convergence of output error identification algorithms

Abstract

In this work, a new off-line optimization approach is proposed to improve the global convergence. This algorithm, called Pseudo-Output Error (POE) algorithm, is based on the introduction of a stationary filter in the parametric sensitivity functions of the Gauss-Newton algorithm. The global convergence is assured for a first order system, what ever the stationary filter of the same order. Consequently, a partial fraction expansion of an nth order system into n first order systems in parallel is introduced. The identification of each individual system using the POE algorithm is globally convergent. The expansion introduces a filtering process and uses an a priori knowledge on the parameters that can bias the estimation process. However, the estimated parameters are close to the true parameters and are used to initialize the Gauss-Newton Output Error (OE) algorithm. The results of the performed simulations show the efficiency of the proposed approach. In particular, while the traditional OE algorithm diverges when it is applied directly to the system to be identified, the POE algorithm in conjunction with the decomposition of the system leads to a very good initialization for the OE algorithm. Consequently, the latter algorithm converges to the true parameters.