Adaptive dynamic surface control of pure-feedback nonlinear systems in pseudo-affine form

This paper is concerned with the robust tracking control for a class of SISO pure-feedback nonlinear systems in pseudo-affine form. Under the lowly restrictive assumption that the bounds of each unknown nonlinearities can be expressed by a known function multiplied by an unknown parameter, an approximation-free adaptive dynamic surface control (DSC) scheme is developed. Through Lyapunov synthesis, it is shown that the developed scheme can guarantee semi-global uniform ultimate boundedness of all closed-loop signals and make the convergence of the output tracking error to an arbitrarily small residual set. Numerical simulation studies are given to demonstrate the effectiveness of the proposed approach.