MODEL REDUCTION IN RECURSIVE LEAST SQUARES IDENTIFICATION

A method to reduce an overparameterized ARX model obtained through least squares identification is presented. The method needs only data directly or easily obtained during a recursive identification of the large model, thus making it well suited to be used in adaptive control. The parameters of the reduced models can be viewed of as Markov estimates of the true parameters (assumed included in the selected structure), with the parameters of the large model interpreted as noisy measurements of these parameters. The method tries to find the smallest model with parameters within specified confidence intervals of the parameters of the large model. Two versions of the method are given. The first estimates the delay and the orders of both the transfer function polynomials. The second method needs significantly less computation, but does not estimate the delay, and will in general only estimate the order of one of the polynomials correctly, which is enough to eliminate the possibility for common factors.