Consistent Nonparametric Estimation of NARX Systems Using Convex Optimization

In this paper, a nonparametric method based on quadratic programming (QP) for identification of nonlinear autoregressive systems with exogenous inputs (NARX systems) is presented. We consider a mixed parametric/nonparametric model structure. The output is assumed to be the sum of a parametric linear part and a nonparametric Lipschitz continuous part. The consistency of the estimator is shown assuming only that an upper bound on the true Lipschitz constant is given. In addition, different types of prior knowledge about the system can easily be incorporated. Examples show that the method can give accurate estimates also for small data sets and that the estimate of the linear part sometimes can be improved compared to the linear least squares estimate.