Adaptive Neural Networks Control for Variable-Order Fractional Nonlinear Systems with Input Saturation

The adaptive neural networks (NNs) tracking control issue is studied for a class of variable-order fractional systems (VOFSs) with input saturation. By introducing a disturbance-like term, the difficulty that comes from incommensurate derivative order in system is successfully overcome. Compared with literature, the boundedness assumption of disturbance-like term is removed in this paper. Then, by using the backstepping method, the adaptive control scheme is designed and the stability of system is analyzed. It is worth pointing out that the derivative order of parameter update laws is independent of the one of system. Besides, a new auxiliary filter signal is proposed to deal with input saturation. Finally, the effectiveness of proposed control scheme is illustrated by numerical simulations.