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

Published online by Cambridge University Press:  04 September 2014

JIANPING CAI,
LUJUAN SHEN and
FUZHEN WU
JIANPING CAI
Affiliation:
Zhejiang University of Water Resource and Electric Power Hangzhou, 310018, P.R.China
LUJUAN SHEN
Affiliation:
Zhejiang University of Water Resource and Electric Power Hangzhou, 310018, P.R.China
FUZHEN WU
Affiliation:
Zhejiang University of Water Resource and Electric Power Hangzhou, 310018, P.R.China
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Abstract

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

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