Global EPD regulation of uncertain nonlinear systems without global normal forms

Abstract

AbstractThis article considers the global regulation problem for a class of non‐affine nonlinear uncertain systems. We will investigate the extended proportional‐derivative (EPD) controller together with its parameters design. The EPD controller is the natural extension of the classical PD control, which adjusts the input signal by using the regulation error together with its derivatives only. We will show that under some suitable conditions on nonlinearity and uncertainty of the systems, the regulation error of the closed‐loop system will converge to 0 exponentially, provided that the EPD controller parameters are chosen from an n‐dimensional unbounded set constructed in the article. In contrast to most of the existing literature on controller design of nonlinear systems, we do not require such special system structures as normal or triangular forms. We will also give an example where the regulation problem is solvable globally by the classical PD control, while the controlled system cannot be transformed into the nonlinear normal form globally.