Multiple model approach to nonlinear system identification with an uncertain scheduling variable using EM algorithm

This paper deals with system identification of general nonlinear dynamical systems with an uncertain scheduling variable. A multi model approach is developed; wherein, a set of local auto regressive exogenous (ARX) models are first identified at different process operating points, and are then combined to describe the complete dynamics of a nonlinear system. An expectation-maximization (EM) algorithm is used for simultaneous identification of local ARX models, and for computing the probability associated with each of the local ARX models taking effect. A smoothing algorithm is used to estimate the distribution of the hidden scheduling variables in the EM algorithm. If the dynamics of the scheduling variables are linear, Kalman smoother is used; whereas, if the dynamics are nonlinear, sequential Monte-Carlo (SMC) method is used. Several simulation examples, including a continuous stirred tank reactor (CSTR) and a distillation column, are considered to illustrate the efficacy of the proposed method. Furthermore, to highlight the practical utility of the developed identification method, an experimental study on a pilot-scale hybrid tank system is also provided.