Adaptive NN control of uncertain nonlinear pure-feedback systems

This paper is concerned with the control of nonlinear pure-feedback systems with unknown nonlinear functions. This problem is considered di/cult to be dealt with in the control literature, mainly because that the triangular structure of pure-feedback systems has no a/ne appearance of the variables to be used as virtual controls. To overcome this di/culty, implicit function theorem is 0rstly exploited to assert the existence of the continuous desired virtual controls. NN approximators are then used to approximate the continuous desired virtual controls and desired practical control. With mild assumptions on the partial derivatives of the unknown functions, the developed adaptive NN control schemes achieve semi-global uniform ultimate boundedness of all the signals in the closed-loop. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. ? 2002 Elsevier Science Ltd. All rights reserved.