Robust Adaptive Control for a class of uncertain nonlinear systems with an optimized smooth input

Modeling uncertainties and disturbances in physical systems seriously deteriorate the tracking performance. In this paper, a modified robust adaptive control strategy is proposed for a class of uncertain nonlinear systems, in which all kinds of uncertainties (i.e., parametric uncertainties, unconsidered dynamics and external disturbance) can be handled simultaneously. The robust control law is developed by an improved form, which can ensure the input continuous thoroughly, to attenuate the lumped uncertainties including unconsidered dynamics and external disturbances. In addition, a smooth projection mapping is used at each step of the adaptive backstepping design procedure to ensure the boundedness of parameter estimation. The developed controller does not require the prior knowledge of the bound of any uncertainty. The stability of the whole closed-loop system is obtained, and the global asymptotic output performance can also be guaranteed. Comparative simulation results are provided to illustrate the effectiveness of the proposed control scheme.