Backstepping Adaptive Control of a Class of Uncertain Nonlinear System

This paper presents two backstepping adaptive controller design schemes for a class of uncertain nonlinear single-input-single-output system with unknown interval backlash-like hysteresis.In the first scheme,a sign function is involved which can ensure perfect tracking.To avoid possible chattering caused by the sign function,an alternative smooth control law is proposed,so that the tracking error still approach a prescribed bound.Unlike some existing control schemes,the developed backstepping controls do not require the model parameters within known intervals and the knowledge on the bound of disturbance-like term.Besides illustrating global stability,an explicit bound on the L2 performance of the tracking error in terms of design parameters is given.Simulation results prove the effectiveness of the design schemes.