Adaptive nonlinear control for a class of pure-feedback systems

An adaptive nonlinear control method is developed for a class of completely nonaffine pure-feedback systems by the combination of back-stepping design and singular perturbation theory. This strategy can simplify the back-stepping design for the control of pure-feedback system by eliminating the problem of “explosion of complexity”. The virtual/actual control input is derived from the solution of a fast dynamical equation with a parameter estimator subject to parameter projection. It is shown that the proposed approach can ensure boundedness of all the signals in the closed-loop system. The tracking error can be made arbitrarily small by choosing appropriate design parameters. Tracking performance is illustrated by simulation results.