Direct adaptive neural control of completely non-affine pure-feedback nonlinear systems with small-gain approach

In this paper, direct adaptive neural tracking control is proposed for a class of completely non affine pure feedback nonlinear systems with only one mild assumption on affine terms, which are obtained using implicit function theorem and mean value theorem. To effectively remove the restriction of the upper bound on the affine terms, a smooth function is introduced to compensate the interconnected term of the former step in backstepping design. The proposed control scheme can not only guarantee the boundedness of all the signals in the closed loop system and the tracking performance, but also provide a simple and effective way for controlling non affine pure feedback systems with a mild assumption. Simulation studies are given to demonstrate the effectiveness of the proposed scheme.