Local modelling with a priori known bounds using direct weight optimization

In local modelling, function estimates are computed from observations in a local neighborhood of the point of interest. A central question is how to choose the size of the neighborhood. Often this question has been tackled using asymptotic (in the number of observations) arguments. The recently introduced direct weight optimization approach is a non-asymptotic approach, minimizing an upper bound on the mean squared error. In this paper the approach is extended to also take a priori known bounds on the function and its derivative into account. It is shown that the result will sometimes, but not always, be improved by this information. The proposed approach can be applied, e.g., to prediction of nonlinear dynamic systems and model predictive control.