In this paper, the adaptive fuzzy backstepping control problem is considered for a class of single-input single-output (SISO) unknown uncertain nonaffine nonlinear systems in strict-feedback form. Within this approach, Nussbaum gain functions are introduced to solve the problem of unknown control directions. The unknown nonlinear functions are approximated by employing adaptive fuzzy systems. The stability analysis of the closed-loop system in the sense of Lyapunov guarantees the global boundedness property for all the signals and states, and at the same time, steers the tracking error to a small neighborhood of the origin. The feasibility of the developed control approach is illustrated by numerical simulation.

在本文中，对于一类单输入单输出（SISO）未知不确定非仿射非线性系统，严格反馈形式考虑自适应模糊反步控制问题。在这种方法中，引入了 Nussbaum 增益函数来解决未知控制方向的问题。采用自适应模糊系统对未知非线性函数进行逼近。李雅普诺夫意义上的闭环系统稳定性分析保证了所有信号和状态的全局有界性，同时将跟踪误差引导到原点的一个小邻域。数值模拟说明了所开发的控制方法的可行性。