In this study, an adaptive fuzzy output tracking control scheme is proposed for uncertain strict-feedback systems with unknown control directions. Nussbaum-type functions are designed, with which the effects of multiple unknown control directions can be handled. Compared with the existing Nussbaum-type functions dealing with the same problem, the proposed Nussbaum-type functions have smaller amplitudes that are more conducive to the design of the controller. Fuzzy functions are used to estimate the unknown terms by combining adaptive laws with backstepping procedure. Adaptive fuzzy controller is constructed to guarantee that the output tracking error system is asymptotically stable and all states in the closed-loop system are bounded. Finally, numerical simulation studies are presented to illustrate the effectiveness of the proposed criteria.

本文针对控制方向未知的不确定严格反馈系统，提出了一种自适应模糊输出跟踪控制方案。设计了Nussbaum类型的函数，可以处理多个未知控制方向的影响。与处理相同问题的现有Nussbaum型函数相比，所提出的Nussbaum型函数具有较小的幅度，更有利于控制器的设计。模糊函数用于通过将自适应定律与反推过程相结合来估计未知项。自适应模糊控制器的构造可确保输出跟踪误差系统渐近稳定，并且闭环系统中的所有状态都是有界的。最后，数值模拟研究表明了提出的标准的有效性。