This paper aims at putting forward an adaptive fuzzy hierarchical sliding mode control method to deal with the control problem for uncertain under-actuated switched nonlinear systems with actuator faults. First, both the bias fault and the loss of effectiveness are considered for the actuator faults. Then, the unknown uncertain functions of the under-actuated switched nonlinear system are approximated by utilising the approximation ability of fuzzy logic systems (FLSs). The error terms caused by FLSs and the upper bound of the bias signal of the actuator faults are integrated into a function where the upper bound of the function is on-line estimated. Furthermore, the singular problem of denominators can be well solved by introducing the projection algorithm. Based on our proposed control scheme, the boundedness of all the signals in the closed-loop system can be verified by resorting to the Lyapunov stability theory. Finally, a simulation example is given to verify the effectiveness of the proposed control scheme.

本文旨在提出一种自适应模糊层次滑模控制方法，以解决具有执行器故障的不确定欠驱动切换非线性系统的控制问题。首先，对于执行器故障，既要考虑偏置故障，又要考虑有效性的损失。然后，利用模糊逻辑系统（FLSs）的逼近能力，对欠驱动切换非线性系统的未知不确定函数进行逼近。由FLS和执行器故障的偏置信号的上限引起的误差项被集成到一个函数中，该函数的上限是在线估计的。此外，通过引入投影算法可以很好地解决分母的奇异问题。根据我们提出的控制方案，闭环系统中所有信号的有界性可以通过利雅普诺夫稳定性理论来验证。最后，给出了一个仿真实例来验证所提出的控制方案的有效性。