New results on recursive identification of NARX systems

Abstract

Recursive identification of nonlinear autoregressive system with exogenous inputs (NARX) yk + 1 = f(yk, ldots, y, uk, …, u) + ek + 1 is considered in this paper. Continuing a work on the same topic by the authors, the present paper covers a larger class of systems, uses less restrictive conditions, and provides deeper results. To be specific, first, by weakening conditions imposed on f(·) the class of systems has significantly been enlarged, for example, it now covers the Hammerstein system as a special case. Second, a technical condition has been removed that was previously imposed on the function coefficient characterizing the rate of convergence to the invariant measure. Third, not only the strong consistency but also the convergence rate of estimates have been established. The behavior of the estimates is demonstrated by some numerical examples. In particular, when applying to a Hammerstein system, the estimate given in this paper is put in a comparison with the Yule–Walker equation-based identification algorithms existing in the literature. Copyright © 2011 John Wiley & Sons, Ltd.