Adaptive Control for Uncertain Hysteretic Systems

Abstract

This paper presents an approach to use the L1 adaptive controller for a class of uncertain systems in the presence of unknown Preisachtype hysteresis in input, unknown timevarying parameters, and unknown timevarying disturbances. The hysteresis operator can be transformed into an equivalent linear timevarying (LTV) system with uncertainties, which means that the effect of the hysteresis can be considered as general uncertainties to the system. Without constructing the inverse hysteresis function, the L1 adaptive control is used to handle the uncertainties introduced by the hysteresis, as well as system dynamics. The adaptive controller presented in this paper ensures uniformly bounded transient and tracking performance for uncertain hysteretic systems. The performance bounds can be systematically improved by increasing the adaptation rate. Simulation results with Preisachtype hysteresis are provided to verify the theoretical findings.