Redesign of approximate dynamic inversion for pure-feedback nonaffine-in-control nonlinear systems via input saturation

Abstract

In this paper, a redesigned approximate dynamic inversion (RADI) method is developed for a class of pure-feedback nonaffine-in-control nonlinear systems (PFNNSs). Recently, the approximate dynamic inversion (ADI)-based algorithms have been widely implemented for nonaffine-in-control nonlinear systems. To employ ADI-based methods, a fast dynamic subsystem has to be established to derive the explicit inversion of the nonaffine equation. However, the previous research on ADI rarely considers that the amplitude of actual input derived from the fast augmented subsystem can be extremely high, which maybe intolerable for practical systems. In this paper, we set up input saturation and view the difference between input with and without saturation as a perturbation. Then, an intermediate subsystem is constructed to compensate the influence of this perturbation by approximating its inversion. The exponential stability of the overall closed-loop system is ensured via singular perturbation theorem. Numerical examples are provided to demonstrate the effectiveness of the proposed method.