Adaptive Dynamic Surface Control of a Class of Nonlinear Systems with Unknown Duhem Hysteresis

Abstract

In this paper, the tracking problem for a class of uncertain perturbed strict-feedback nonlinear systems with unknown Duhem hysteresis input is investigated. Different with the conventional nonlinear systems, the existence of the unknown preceded hysteresis will affect the system performance and bring a challenge for the controller design. To overcome the difficulties caused by the unknown hysteresis, the Duhem model is used to describe the hysteresis in this paper. The properties of the Duhem model are utilized to get the explicit expression of the hysteresis output, which makes it possible to deal with the unknown hysteresis input. Following the conventional backstepping design procedure, a dynamic surface control method in each step is used to avoid “the explosion complexity” in the backstepping design, and the Nussbaum function method is used to solve the time-varying coefficient problem in the explicit expression of the Duhem model. Under the proposed control approach, the semiglobal uniform ultimate boundedness of all the signals in the close-loop system is guaranteed. The effectiveness of the proposed design scheme is validated through a simulation example.KeywordsNonlinear systemshysteresisdynamic surface control