Identification of dynamical systems under multiple operating conditions via Functionally Pooled ARMAX models

In a companion paper [1], a novel framework for the identification of stochastic dynamical systems under multiple operating conditions, with each condition characterized by a measurable variable, is introduced and used for the identification of postulated Functionally Pooled AutoRegressive with eXogenous input (FP-ARX) models. The present paper focuses on the use of this framework for the identification of FP-ARMAX models, which additionally incorporate Moving Average (MA) part. FP-ARMAX models are conceptual extensions of their conventional ARMAX counterparts, with the important difference that their parameters and innovations variance are functions of the measurable variable and that they account for cross-correlations among the operating conditions. Yet, FP-ARMAX model identification is more complicated, and is presently achieved via Prediction Error and Maximum Likelihood type methods. The asymptotic properties of the Prediction Error estimator are established, and the estimators' performance characteristics are assessed via a Monte Carlo study.