An adaptive fuzzy control approach is proposed for nonaffine pure-feedback systems with nonaffine functions being semibounded and possibly indifferentiable. A semibounded and continuous condition for nonaffine function is presented to guarantee the controllability of system. To overcome the difficulty from this mild condition, a compact set is introduced, and the nonaffine nonlinear functions are modeled in a new way based on this compact set, which is proved to be invariant set eventually. By using the dynamic surface control (DSC) technique, the problem of explosion of complexity inherent in backstepping method is avoided in the proposed adaptive fuzzy control scheme. Robust compensators are used to minify the influence of uncertainties and disturbances. Furthermore, it is proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.

中文翻译：

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半有界不可微非仿射函数纯反馈非线性系统的自适应模糊控制

针对非仿射函数半有界且可能不可微的非仿射纯反馈系统，提出了一种自适应模糊控制方法。为保证系统的可控性，提出了非仿射函数的半有界连续条件。为了克服这种温和条件带来的困难，引入了一个紧集，并基于这个紧集以一种新的方式对非仿射非线性函数进行建模，最终证明它是不变集。通过使用动态表面控制 (DSC) 技术，所提出的自适应模糊控制方案避免了反步法固有的复杂性爆炸问题。稳健补偿器用于最小化不确定性和干扰的影响。此外，证明了所有闭环信号都是有界的，跟踪误差渐近收敛到一个小的残差集。最后，通过仿真实例验证了所设计方法的有效性。