针对一类具有严格反馈形式的不确定分数阶非线性系统,提出了一种自适应模糊滑模反步控制方法。根据反步控制原理, 首先在每一步中, 利用模糊逻辑系统逼近系统的未知部分, 然后构造一种分数阶积分型滑模面, 依据滑模控制理论来进行虚拟控制器设计。其次, 设计了一种滤波器用来解决在反步控制中由于对虚拟控制器反复求导而产生的“项数爆炸”问题。基于Lyapunov分数阶稳定性理论, 对误差动力系统进行稳定性分析,确保追踪误差最终能够收敛到原点附近一个可以调整的邻域。最后, 给出一个仿真实例来验证该方法的有效性。

The control problem of a class of uncertain fractional-order nonlinear systems with strict feedback form are studied. According to the backstepping control principle, firstly in each step, the fuzzy logic system is used to approximate the unknown part of the system, and then a fractional integral sliding mode surface is constructed, and the virtual controller design of each step is carried out according to the sliding mode control theory. Secondly, a filter is designed to solve the problem of “explosion of complexity” caused by repeated derivative of the virtual controller in the backstepping control. Based on the Lyapunov fractional stability theory, the stability analysis of the error dynamic system is carried out to ensure that the tracking error eventually converges to a neighborhood with an adjustable neighborhood near the origin. Finally, a simulation example is given to verify the effectiveness of the method.