Adaptive backstepping control of a class of unknown backlash-like hysteresis Nonlinear systems

This note presents a backstepping adaptive controller design schemes for a class of uncertain nonlinear single-input-single-output system preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation, in the presence of bounded external disturbances. In the scheme, we propose an alternative smooth control law and the tracking error is still ensured to approach a prescribed bound in this case. 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 is not required. Besides showing global stability, we also give an explicit bound on the L2 performance of the tracking error in terms of design parameters. Simulation results illustrates the effectiveness of our schemes.