Adaptive control of a class of non-linear systems preceded by backlash-like hysteresis

摘要

We consider a class of uncertain non-linear systems preceded by unknown backlash-likernhysteresis, which is modelled by a differential equation. We propose a new state feedbackrnrobust adaptive control scheme using a backstepping technique and properties of therndifferential equation. In this control scheme, we construct a new continuous function torndesign an estimator to estimate the unknown constant parameters and the unknown boundrnof a ‘disturbance-like’ term. The transient performance of the output tracking error can bernguaranteed by the introduction of pre-estimates of the unknown parameters in ourrncontroller together with update laws. We do not require bounds on the ‘disturbance-like’rnterm or unknown system parameters in this scheme. The global stability of the closed-looprnsystem can be proved.