Adaptive Neural Control for Nonaffine Pure-Feedback System Based on Extreme Learning Machine

For nonaffine pure-feedback systems, an adaptive neural control method based on extreme learning machine (ELM) is proposed in this paper. Different from the existing methods, this scheme firstly converts the original system into a nonaffine system containing only one unknown term by equivalent transformation, thus avoiding the cumbersome and complex indirect design process of traditional backstepping methods. Secondly, a high-performance finite-time-convergence-differentiator (FD) is designed, through which the system state variables and their derivatives are accurately estimated to ensure the control effect. Thirdly, based on the implicit function theorem, the ELM neural network is introduced to approximate the uncertain items of the system, which simplifies the repeated adjustment process of the network training parameters. Meanwhile, the minimum learning parameter algorithm (MLP) is adopted to design the adaptive law for the norm of the network weight vector, which significantly reduces calculations. And it is theoretically proved that the closed-loop control system is stable and the tracking error is bounded. Finally, the effectiveness of the designed controller is verified by simulation.