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The dynamic surface control (DSC) technique was developed recently by Swaroop et at This technique simplified the backstepping design for the control of nonlinear systems in strict-feedback form by overcoming the problem of "explosion of complexity?' It was later extended to adaptive backstepping design for nonlinear systems with linearly parameterized uncertainty. In this paper, by incorporating this design 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 strict-feedback form with arbitrary uncertainty. Our development is able to eliminate the problem of "explosion of complexity" inherent in the existing method. In addition, 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. [ABSTRACT FROM AUTHOR]