Adaptive dynamic surface controller design for a class of pure-feedback nonlinear systems with Backlash-like hysteresis

Focusing on a class of pure-feedback nonlinear time-delay systems with unknown hysteresis input, an adaptive control method is discussed in this paper. For such nonlinear systems, the nonaffine structure and the non-smooth hysteresis nonlinearities are the major challenges for the controller design. To deal with the nonaffine problem of pure-feedback systems, mean-value theorem is adopted to transform the systems as affine form, and neural network approximator is utilized to estimate the unknown system functions. For the unknown preceded hysteresis nonlinearities, the Backlash-like model is utilized as an illustration to show the way dealing with the unknown hysteresis input. Following the backstepping design procedure, a dynamic surface control approach is investigated to avoid the complexity of controller by applying the low-pass filters at each step, and the semiglobal uniform ultimate boundedness of the signals in the closed-loop system is ensured. The proposed control method explores the validity mitigating the negative effects caused by the unknown hysteresis, and the simulation results validate the effectiveness of the proposed design scheme.