Adaptive output feedback control of linear systems preceded by unknown backlash-like hysteresis

In this paper, a new scheme is proposed to address an output feedback control problem: control of a class of uncertain linear systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modelled by a differential equation as in (C.Y. Su et al., 2000). The controller designed by using backstepping technique consists of a new robust control law and a new estimator to estimate the unknown parameters. For the implementation of the controller, no knowledge is assumed on the bounds of unknown system parameters and the effect contributed by the hysteresis. It is shown that all the signals are bounded. A bound for the truncated L₂ norm of the tracking error is obtained as a function of design parameters. Simulation studies also verify the effectiveness of the proposed scheme.