Nonparametric Modeling of Mutually Ambiguous Mappings

Abstract

This paper considers the problem of approximating a function from observations in the case when the object under study contains mutually ambiguous characteristics in its description. This formulation is essential in identifying and controlling systems of the Wiener and Hammerstein class, in which nonlinear processes can be represented as a sequential connection of linear dynamic and nonlinear inertia-free blocks. Often elements such as hysteresis loop, backlash and others are used as nonlinear blocks. These elements are mutually ambiguous mappings. In connection with the transition to automated digital production, which is controlled in real time by intelligent systems rather than humans, nonlinear dynamic processes are found everywhere. The complexity of solving the problem lies in the lack of sufficient a priori information about the parametric structure of the model of the process under study. The paper proposes some modifications of the nonparametric estimation of the regression function, allowing for the modeling of mutually ambiguous mappings. Some fragments of numerical studies are presented that show acceptable results in terms of reconstruction accuracy.