Adaptive Dynamic Surface Control for A Class of Uncertain Nonlinear Systems in Pure-Feedback Form

In this paper, by incorporating the dynamic surface control technique into a neural network based adaptive control design framework, we have developed a backstepping based control design for a class of nonlinear systems in pure-feedback form with arbitrary uncertainty. Our development is able to eliminate the problem of "explosion of complexity" inherent in the existing method. In addition, the circular design problem which exist in pure-feedback systems is overcome. A stability analysis is given which shows that our control law can guarantee the uniformly ultimate boundedness of the solution of the closed-loop system, and make the tracking error arbitrarily small. Moreover, the proposed control design scheme can also be directly applied to the strict-feedback nonlinear systems with arbitrary uncertainty.