From Data to Nonlinear Predictive Control. 1. Identification of Multivariable Nonlinear State Observers

Abstract

This work aims at the identification of a special class nonlinear state space observers for nonlinear multivariable systems directly from input−output data when the data is corrupted with unmeasured disturbances. At the identification stage, the one step ahead predictor form of the model is arranged to have a Weiner-like structure. The linear dynamic component of the predictor is parametrized using generalized orthonormal basis functions. The resulting observer is shown to be a nonlinear ARX (NARX) type model with an infinite but fading memory property. It is also shown that the proposed model structure is capable of capturing input as well as output multiplicity (multiple steady states) behavior. The efficacy of the proposed modeling scheme is demonstrated using simulation studies on a continuously stirred tank reactor (CSTR) process model, which exhibits input multiplicity, and another CSTR process model that exhibits output multiplicities. The types of unmeasured disturbances investigated are (a) unkno...