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Adaptive Control for Uncertain Continuous-Time Systems Using Implicit Inversion of Prandtl-Ishlinskii Hysteresis Representation

In this note, an implicit inversion approach is introduced to avoid difficulties associated with stability analysis in the direct application of inversion for operator-based hysteresis models. Based on this implicit inversion, an adaptive control algorithm is formulated for continuous-time linear dynamical systems preceded with hysteresis nonlinearities described by the Prandtl-Ishlinskii model. A stability analysis of the controlled system is performed to show that zero-output tracking error can be achieved. Simulation results show the effectiveness of the proposed algorithm.