Adaptive control of a class of uncertain nonlinear systems with unknown input hysteresis

Based on backstepping technique, an adaptive inverse control scheme is proposed for a class of uncertain nonlinear systems preceded by unknown hysteretic nonlinearities which are described by Krasnosel´skii-Pokrovkii (KP) model. The pseudo-inversion is introduced to compensate the hysteresis nonlinearities and the error caused by the hysteresis model and pseudo-inversion is estimated online by the adaptive controller. To avoid the possible chattering caused by the sign function, a smooth adaptive controller is designed. The proposed controller ensures the uniformly ultimate boundedness of the closed-loop system. Simulation results show the effectiveness of the proposed scheme.