A fractional-order integral fuzzy sliding mode control scheme is proposed for a class of uncertain fractional-order nonlinear systems subject to uncertainties and external disturbances. First, in each step, a neuro-fuzzy network system is developed to approximate the uncertain nonlinear function existing in fractional-subsystem and a fractional sliding mode surface is presented. Second, based on the fractional Lyapunov stability theory and the finite-time stability theory, a fractional adaptive backstepping neuro-fuzzy sliding mode controller is designed to drive the state trajectories of fractional-order systems to the prescribed sliding mode surface. Meanwhile, the finite-time stability of the fractional-order closed-loop system is proved. At last, three numerical examples are given to illustrate the effectiveness of the proposed control method.

中文翻译：

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基于有限时间方案的不确定分数阶非线性系统的自适应反步混合模糊滑模控制

针对一类受不确定性和外部扰动影响的不确定分数阶非线性系统，提出了一种分数阶积分模糊滑模控制方案。首先，在每一步中，开发一个神经模糊网络系统来逼近分数子系统中存在的不确定非线性函数，并提出分数滑模面。其次，基于分数阶Lyapunov稳定性理论和有限时间稳定性理论，设计了分数阶自适应反推神经模糊滑模控制器，将分数阶系统的状态轨迹驱动到规定的滑模面。同时证明了分数阶闭环系统的有限时间稳定性。最后，给出三个数值例子来说明所提出的控制方法的有效性。