Robust Identification of Piecewise/Switching Autoregressive Exogenous Process

A robust identification approach for a class of switching processes named PWARX (piecewise autoregressive exogenous) processes is developed in this article. It is proposed that the identification problem can be formulated and solved within the EM (expectation-maximization) algorithm framework. However, unlike the regular EM algorithm in which the objective function of the maximization step is built upon the assumption that the noise comes from a single distribution, contaminated Gaussian distribution is utilized in the process of constructing the objective function, which effectively makes the revised EM algorithm robust to the latent outliers. Issues associated with the EM algorithm in the PWARX system identification such as sensitivity to its starting point as well as inability to accurately classify "un-decidable" data points are examined and a solution strategy is proposed. Data sets with/without outliers are both considered and the performance is compared between the robust EM algorithm and regular EM algorithm in terms of their parameter estimation performance. Finally, a modified version of MRLP (multi-category robust linear programming) region partition method is proposed by assigning different weights to different data points. In this way, negative influence caused by outliers could be minimized in region partitioning of PWARX systems. Simulation as well as application on a pilot-scale switched process control system are used to verify the efficiency of the proposed identification algorithm. (C) 2009 American Institute of Chemical Engineers AIChE J, 56: 1829-1844, 2010