Tracking Control for a Class of Uncertain Nonlinear Affine Systems via Discontinuous Feedbacks

Abstract

Tracking control is investigated for a class of uncertain nonlinear systems, affine in the control To encompass all possible realizations of uncertainty, the systems are described by differential inclusions and the uncertain systems are modelled as nonlinear perturbations to a known nonlinear affine control system. The nonlinear tracking problem is converted to the problem of stabilizing nonlinear time-varying systems and a class of discontinuous feedback controls is developed such that the uncertain nonlinear system tracks desired trajectories to the zero state. The design of such feedbacks is based on a deterministic control methodology which does not require full identification of uncertain elements but does require a knowledge of structural properties and bounds relating to the uncertainty.