Vector-dependent Functionally Pooled ARX Models for the Identification of Systems Under Multiple Operating Conditions

The identification of stochastic systems operating under multiple conditions is addressed based on data records obtained under a sample of these conditions. The problem is important in many practical applications and is tackled within a recently introduced Functional Pooling framework. The study focuses on the case of operating conditions characterized by several parameters. Global Vector-dependent Functionally Pooled models of the ARX type are postulated, proper estimators based on the Least Squares and Maximum Likelihood principles are formulated, and their strong consistency and asymptotic normality are established. For model structure selection a Genetic Algorithm based procedure is formulated. The performance characteristics of the methods are assessed via a Monte Carlo study.