Adaptive neural network finite-time control for fractional-order nonlinear systems with external disturbance

This paper is concerned with the finite-time tracking control problem of fractional-order nonlinear systems (FONSs) with uncertainty and external disturbance. A novel design scheme of the adaptive neural network finite-time controller (ANNFTC) is developed by utilizing the theory of finite-time stability and fractional-order dynamic surface control (DSC) scheme combined with backstepping method. Radial basis function neural networks (RBF NNs) are employed to estimate the unknown nonlinear function. Furthermore, an auxiliary function is introduced to approximate the unknown upper bounds of the approximation error in RBF NNs and external disturbance. The ANNFTC ensures the finite-time boundedness of all signals in FONSs and enhances the system output's tracking performance. The effectiveness of the proposed approach is demonstrated through a simulation example, providing empirical evidence to support the theoretical framework presented in this paper.