Robust Tracking Control for a Class of Uncertain Systems with Matched and Unmatched Nonlinearities*

Abstract

This article is concerned with the systematic design of robust nonlinear tracking controllers with various degrees of aggressiveness for a certain class of uncertain systems i.e. systems which are nominally linear, suffering from matched model uncertainties and disturbances and uncertain matched and unmatched nonlinearities. The proposed composite state feedback tracking controller u = uL+uN consists of two parts: a linear and a nonlinear one. The LMI–based design of the linear part of the composite controller is based on the nominal linear system and is formulated as a multi–objective H∞ minimization problem for stabilization, disturbance rejection, tracking, performance and minimization of the 2-norm of the state feedback gains. The design of the nonlinear part is based on Lyapunov redesign methodologies, and a continuous nonlinear state feedback guarantees Uniform Ultimate Boundedness (UUB) of the closed–loop system. Explicit formulae for the size of the UUB region and the Radius of the Attracting Ball (RAB) are derived, indicating a tradeoff between robustness, tracking performance and control chattering. The efficacy of the proposed methodology is demonstrated in a numerical example on a single input system.