Dynamic surface control for a class of nonlinearly parameterized systems with input time delay using neural network

By using the radial basis function neural network (RBF NN), this paper presents tracking control problem of the nonlinear systems with the input time delay, in which the unknown continuous functions may be nonlinearly parameterized. Different from the existing results which deal with the nonlinearly parameterized functions by using the separation principle, in this paper, the nonlinearly parameterized functions are lumped into the continuous functions, and then, the neural networks (NNs) are applied to approximate them. Moreover, through a state transformation the system can be easily transformed into a system without the input time delay. Finally, based on the minimal learning parameters (MLP) algorithm and the adaptive backstepping dynamic surface control (DSC) technique, a new adaptive NN backstepping control scheme is developed, and only two parameters need to be adjusted online in the controller design procedure. Thus, the proposed control method cannot only overcome the problem of “explosion of complexity” inherently existing in traditional backstepping design methods, but also reduce the computational burden greatly. It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error can converge to a small neighborhood of the origin with an appropriate choice of design parameters. Finally, three examples are used to show the effectiveness of the proposed approach.