Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis

Abstract—In this note, we consider the same class of systems as in a pre-vious paper, i.e., a class of uncertain dynamic nonlinear systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation, in the presence of bounded external dis-turbances. By using backstepping technique, robust adaptive backstepping control algorithms are developed. Unlike some existing control schemes for systems with hysteresis, the developed backstepping controllers do not re-quire the uncertain parameters within known intervals. Also, no knowledge is assumed on the bound of the “disturbance-like ” term, a combination of the external disturbances and a term separated from the hysteresis model. It is shown that the proposed controllers not only can guarantee global sta-bility, but also transient performance. Index Terms—Adaptive control, backstepping, hysteresis, nonlinear system, robust control. I