This paper proposes a novel fixed-time adaptive general type-2 fuzzy logical control (FAGT2FLC) scheme for an air-breathing hypersonic vehicle (AHV) with uncertainties. Firstly, the AHV dynamic model is transformed into a strict feedback form. Then, the FAGT2FLC is designed based on the transformed model to improve robustness and guarantee fixed-time convergence of the closed-loop system. The general type-2 fuzzy logic system (GT2FLS) is utilized to approximate the model uncertainties; for the purpose of designing adaptive laws, the $\alpha$-plane method is employed to represent the GT2FLS. A parameter projection operator is used to solve the possible singularity problem of parameter adaption. Besides, a fixed-time differentiator is used to deal with the “explosion of terms” inherent in backstepping method. Theoretical analysis based on relevant lemmas shows that the closed-loop system will converge into a small error band in fixed time. Lastly, detailed simulations are carried out to demonstrate the effectiveness and superiority of the proposed control scheme.

本文提出了一种具有不确定性的呼吸高超音速飞行器（AHV）的固定时间自适应通用2型模糊逻辑控制（FAGT2FLC）方案。首先，将AHV动态模型转化为严格的反馈形式。然后，基于变换后的模型设计FAGT2FLC，以提高鲁棒性并确保闭环系统的固定时间收敛。利用通用的2型模糊逻辑系统（GT2FLS）来近似模型的不确定性。为了设计适应性法则，$\alpha$平面法用于表示GT2FLS。参数投影算子用于解决参数自适应可能出现的奇异性问题。此外，使用固定时间微分器来处理反推方法中固有的“术语爆炸”。基于相关引理的理论分析表明，闭环系统将在固定的时间内收敛到一个小的误差带。最后，进行了详细的仿真，以证明所提出的控制方案的有效性和优越性。