Robust adaptive asymptotic tracking control of a class of nonlinear systems with unknown input dead-zone

This paper considers the tracking control for a class of uncertain single-input and single-output (SISO) nonlinear strict-feedback systems with unknown input dead-zone nonlinearity, parametric uncertainties and unknown bounded disturbances. By constructing a smooth dead-zone inverse and applying the backstepping recursive design technique, a robust adaptive backstepping controller is proposed, in which adaptive control law is synthesized to handle parametric uncertainties and a novel robust control law to attenuate disturbances. The robust control law is developed by integrating a sufficiently smooth positive integral function at each step of the backstepping design procedure. In addition, a smooth projection mapping is used and assumptions are made that the prior knowledge of the extents of parametric uncertainties and the variation ranges of the bounds of disturbances is known to facilitate the backstepping recursive design. However, the exact bounds of disturbances are not required. The major feature of the proposed controller is that it can theoretically guarantee asymptotic output tracking performance, in spite of the presence of unknown input dead-zone nonlinearity, various parametric uncertainties and unknown bounded disturbances via Lyapunov stability analysis. Comparative simulation results are obtained to illustrate the effectiveness of the proposed control strategy.