Nonlinear Modeling by Interpolation Between Linear Dynamics and Its Application in Control

Abstract

Abstract This paper proposes a finite series expansion to approximate general nonlinear dynamics models to arbitrary accuracy. The method produces an approximation of nonlinear dynamics in the form of an aggregate of linear models, weighted by unimodal basis functions, and results in a linear growth bound on the approximation error. Furthermore, this paper demonstrates that the proposed approximation satisfies the modeling assumptions for analysis based on linear matrix inequalities and hence widens the applicability of these techniques to the area of nonlinear control.