OVERVIEW OF EMERGING BAYESIAN APPROACH TO NONLINEAR SYSTEM IDENTIFICATION

Over the last twenty years, nonlinear system identiflcation has gained signiflcant interest due to the increasing demand of high performance control. Nonlinear system identiflcation is challenging owing to its complexity, unpre- dictability, and dimension curse. The literature has mainly focused on two classes of modeling. One is the most studied black-box modeling that is completely data based. Another important class of system identiflcation is grey-box modeling, i.e. certain model structure of the underlying system is known, but parameters and state variables are unknown. The general Bayesian approach to nonlinear system identiflcation targets not only the black-box problem but also the grey- box problem. The Bayesian inference idea is certainly not new but its usefulness has not been proven in nonlinear system identiflcation until recent years owing to the increasing capacity of computation power. This paper gives an overview of its most signiflcant development in recent years, namely the unscented Kalman fllter (UKF) for sequential inference of parameters/state. The UKF can be used for on- line as well as ofi-line applications. The general solution to the sequential Bayesian inference problem is flrst reviewed, and the paper will then focus on the unscented Kalman fllter as a representative of the emerging Bayesian flltering approach to system identiflcation. We endeavor to explain mathematical concepts in a simple language and provide a tutorial on some key results. Several engineering examples are presented to illustrate the new developments and their utilities.