In this paper an adaptive control approach for completely non-affine pure-feedback systems with non-linear parameterization is proposed. By using the parameter separation technique and coupling it effectively with combination of backstepping and time scale separation, a fast dynamical equation is derived from the original sub-system, where the solution is sought to approximate the corresponding ideal virtual/actual control input. In this approach, since designing state predictor to derive adaptation law of unknown parameters is omitted, our design is more accurate and less complex. The closed loop stability and the state regulation of nonlinear parameterization pure-feedback systems are all proved by new theorem in singular perturbation theory. Finally the simulation results are provided to demonstrate the effectiveness of the proposed approach.

Keywords