Adaptive control of pure-feedback systems in the presence of parametric uncertainties

Abstract

Abstract:The purpose of this study is to investigate an adaptive control approach for completely nonaffine pure-feedback systems with linear/nonlinear parameterization. In this approach, the parameter separation technique and the idea of the positive function of linearly connected parameters are coupled effectively with the combination of backstepping and time-scale separation. Subsequently, a fast dynamical equation is derived from the original subsystem, where the solution is sought to approximate the corresponding ideal virtual/actual control inputs. Furthermore, the adaptation law of unknown parameters can be derived based on Lyapunov theory in the backstepping technique and there is no need to design a state predictor for this purpose. Therefore, it results in higher accuracy and avoids complexity. The closed-loop stability and the state regulation of these systems are proved. Finally, the simulation results are provided to demonstrate the effectiveness of the proposed approach.