Design of adaptive B-spline neural network controller via backstepping approach

In this paper, a B-spline neural network (BNN) with a set of local basis functions is used to online approximate the unknown nonlinear system dynamics. The BNN has the advantage of locally controlling its network output compared with other neural networks; therefore, it is suitable to online estimate the unknown nonlinear system dynamics. Meanwhile, this paper proposes an adaptive B-spline neural network control (ABNNC) system via backstepping approach for a class of second-order unknown nonlinear plants. A computation controller and a fuzzy compensator are designed in the proposed ABNNC system. The computation controller which is designed in the sense of backstepping approach is the main controller, and the fuzzy compensator is designed to eliminate the effect of the approximation error introduced by the BNN approximator. A parameter adaptation training methodology, which is derived using the Lyapunov stability theorem, is proposed to increase the learning capability of the BNN. Finally, an inverted pendulum system is applied to demonstrate the effectiveness of the proposed ABNNC scheme. The simulation results show that the ABNNC system can achieve good tracking responses without any knowledge of control dynamics.