Adaptive control of non-smooth sandwich systems based on hysteretic operator

Considering the special structure of sandwich system, we present a unit inverse system to compensate for the leading dynamic block of the sandwich system, transforming the sandwich system into a common nonlinear system preceded by hysteresis and disturbance. A novel hysteretic operator is proposed to transform the multi-valued mapping of hysteresis into a one-to-one mapping. Applying the hysteretic operator, we develop an adaptive controller for the sandwich system with hysteresis nonlinearity. The control law and adaptive law are derived from Lyapunov stability theorem, so that the ultimate boundedness of the closed-loop system is guaranteed. Simulation results show the efficacy of the proposed scheme in controlling the sandwich systems with hysteresis.