Padé Approximations and the SDRE Technique in the Design of Parametric Families of Feedback Laws

The paper demonstrates an approach for the construction of a parametric description of a family of feedbacks using one-point and two-point matrix Padé approximations (PA), which are obtained on the basis of asymptotic approximations. The method is demonstrated on numerical calculations for a number of examples from one class of problems with a parameter, and a brief overview of the ideas of using asymptotic approximations in the form of regular series for control problems with continuous perturbations and boundary series is given, in the case of the presence of singular perturbations in the model. Because when constructing matrix PAs and finding matrix coefficients of PAs, linear matrix equations arise, in order to simplify them, Richardson extrapolation is used in the work