ARMAX Augmented UD Identification Algorithm (AUDIX)

Abstract

An ARMAX augmented UD identification (AUDIX) algorithm for systems identification is developed to identify an ARMAX model by rearranging the regressor and parameter vectors and augmenting the covariance matrix of Bierman's UD factorization algorithm. The structure of the AUDIX is particularly easy to interpret and it is a direct extension of the augmented UD identification (AUDI) which is a direct extension to the Recursive Least Squares (RLS) algorithm. The proposed algorithm permits simultaneous identification of model parameters, disturbed by a noise model, plus loss functions for all orders from 1 to n I at each step with approximately the same calculation effort as nth order RLS, in addition it has a fast convergence rate than the AUDI. Simply, this AUDIX algorithm is a least-squares estimator, with the same numerical properties as those of Bierman's UD factorization algorithm. In addition, its structure and implementation are more straightforward and easier to analyze than the UD algorithm. Therefore, the AUDIX provides a convenient and efficient basis to be used on-line in Self-Tuning or adaptive control algorithms. This is because in real applications no guarantee that it will be free from disturbances and measurement noises in addition to stochastic environments. Thus, the objective is to estimate the parameters of the model which best fit a set of observed or measured data. This model is time-varying and is used to determine the parameters of the controller to cope with the changing process characteristics. This algorithm is utilized with the self tuning control of an aeroengine and proved robustness to numerical singularities in addition to fast and good tracking. The paper contains some of the results with a general example showing the good convergence and tracking for this algorithm.