Adaptive inverse control of non-linear systems with unknown complex hysteretic non-linearities

This study addresses the problem of inverse hysteretic compensation for a class of uncertain dynamic non-linear systems preceded by unknown hysteretic non-linearities, where the hysteresis is described by Prandtl–Ishlinskii (P–I) model. First, the continuous P–I hysteresis model is decomposed into a discrete P–I operator and a small-bounded error. Then, the inverse discrete P–I operator is constructed to eliminate the hysteresis effects, and the bounded error is estimated by the controller. To avoid the possible chattering caused by the sign function, a smooth robust adaptive controller with the hyperbolic tangent function is designed based on the backstepping technique. The proposed controller ensures the closed-loop system is uniformly ultimately bounded. Finally, the simulation results demonstrate the effectiveness of the proposed scheme.