Multiple steps prediction with nonlinear ARX models

Abstract

NLARX (NonLinear AutoRegressive with eXogenous inputs) models are frequently used in black-box nonlinear system identification. Though it is easy to make one step ahead prediction with such models, multiple steps prediction is far from trivial. The main difficulty is that in general there is no easy way to compute the mathematical expectation of an output conditioned by past measurements. An optimal solution would require intensive numerical computations related to nonlinear filtering. The purpose of this paper is to investigate simple non optimal prediction methods. It is shown that cautions must be paid when using such methods, since their prediction behaviors may be radically different, depending on some detailed choice.