Adaptive neural control for pure-feedback systems via dynamic surface control approach

This paper proposes a novel dynamic surface control (DSC) algorithm for a class of uncertain nonlinear systems in completely non-affine pure-feedback form. Instead of using the mean value theorem, we construct an affine variable at each design step and then neural network is employed to deduce a virtual control signal or an actual control signal. As a result, the unknown control directions and singularity problem raised by the mean value theorem is circumvented. The proposed scheme is able to overcome the explosion of complexity inherent in backstepping control and dirve the tracking error to converge to an arbitrary small residual set. Moreover, by combining the DSC with the newly developed minimal-learning parameter (MLP) algorithm, it is shown that the design procedure and the computational burden can be greatly reduced. Simulation results are presented to demonstrate the efficiency of the proposed scheme.