I. Introduction
In the past decades, with the development of nonlinear control theory and the demand of practice, the controller design of uncertain nonlinear systems has attracted an increasing attention [1]–[11]. As an effective way to control nonlinear systems, backstepping technique is widely used since it can provide a promising way to improve the transient performance of the systems by tuning design parameters. One problem of backstepping controller is that the repeated high-order derivatives of virtual control laws may result in “explosion of complexity.” To overcome this problem, dynamic surface control (DSC) was first introduced in [12] using a first-order filtering of the synthesized virtual control laws at each step of backstepping procedure. From a practical perspective, the characteristic of nonlinearity is another main issue of nonlinear system control, which also brings some restrictions to the controller design. As shown in [13], the radial basis function neural network (RBF NN) can be considered as a two-layer NN in which the hidden layer performs a fixed nonlinear transformation with no adjustable parameters to map the input space into an intermediate space; then, the output layer combines the outputs of the intermediate layer linearly as the outputs of the whole network. Therefore, they belong to a class of linearly parameterized networks and have well approximation ability. Hence, RBF NN are frequently adopted to deal with these nonlinearities [14]–[16]. In recent years, by combining RBF NN or fuzzy approximation approaches with DSC and backstepping, remarkable results have been done on nonlinear systems in various structures; see, for example, [17]–[22].