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An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network (FTRBFNN) is presented for a general class of strict-feedback nonlinear systems, which may possess a wide class of uncertainties that are not linearly parameterized and do not have any prior knowledge of the bounding functions. FTRBFNN is employed to approximate the uncertainty online, and a systematic framework for adaptive controller design is given by dynamic surface control. The control algorithm has two outstanding features, namely, the neural network regulates the weights, width and center of Gaussian function simultaneously, which ensures the control system has perfect ability of restraining different unknown uncertainties and the integral term of tracking error introduced in the control law can eliminate the static error of the closed loop system effectively. As a result, high control precision can be achieved. All signals in the closed loop system can be guaranteed bounded by Lyapunov approach. Finally, simulation results demonstrate the validity of the control approach.