Robust adaptive control of a class of nonlinear systems with unknown hysteresis nonlinearity

Abstract

In this paper, the tracking problem for a class of uncertain nonlinear systems preceded by unknown Coleman-Hodgdon hysteresis is investigated. By analysing the hysteresis conditions, an important property is given, and hence Coleman-Hodgdon hysteresis can be decomposed as a nonlinear smooth term and a nonlinear bounded distrubance-like term. In order to remove the difficulty arising from the nonlinear smooth term, mean value theorem and a Nussbaum function lemma are introduced. Then following backstepping design procedure, a novel adaptive controller is developed without constructing a hysteresis inverse. The proposed controller not only doesn't need any assumptions on the uncertain system parameters within a known compact and a priori knowledge on the bound of the external disturbance, but also can guarantee global uniformly ultimately boundedness of all signals in the closed-loop system. Simulations performed on a nonlinear system illustrate and clarify the proposed scheme. © 2013 Springer-Verlag Berlin Heidelberg.