This article is considered on underactuated fractional-order stochastic systems (FOSSs) with actuator saturation and incrementally conic nonlinear terms, whose fractional-order $\alpha \in (0,1)$ . First, to bring FO dynamic signals, solving the unmodeled dynamics, in the meantime, the saturated nonlinear term of the control input is taken into account. At the time, to cope with the stability issue of FOSS under such situation, the fault tolerant resilient controller based on underactuated condition is designed. Then, according to the method of the Lyapunov and ${\mathrm{ It}}\hat {\mathrm{ o}}$ differential formulation to design proper multiple Lyapunov–Krasovskii (L-K) functions, such that, a novel sufficient condition of the robustly asymptotically stability of fuzzy FOSS under underactuated conditions is rigorously proved in terms of linear matrix inequality (LMI). Furthermore, in order to research the mean square stability of the above-mentioned system, so the solution of FOSS is obtained to achieve this purpose. By applying the above method, which is proposed in this work that the controlled system can be obtained with faster response and higher control accuracy. At last, to display the superiority of the above-mentioned scheme is effective, tethered satellite system and numerical results are presented.

中文翻译：

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具有未建模动力学和执行器饱和的分数阶随机欠驱动系统的容错模糊弹性控制

本文考虑的是具有执行器饱和和增量圆锥非线性项的欠驱动分数阶随机系统 (FOSS)，其分数阶 $\alpha \in (0,1)$ 。首先，引入FO动态信号，求解未建模的动力学，同时考虑控制输入的饱和非线性项。当时，为了解决FOSS在这种情况下的稳定性问题，设计了基于欠驱动条件的容错弹性控制器。然后根据李亚普诺夫方法 ${\mathrm{ 它}}\hat {\mathrm{ o}}$微分公式设计适当的多个 Lyapunov-Krasovskii (LK) 函数，从而根据线性矩阵不等式 (LMI) 严格证明欠驱动条件下模糊 FOSS 鲁棒渐近稳定性的新充分条件。此外，为了研究上述系统的均方稳定性，因此得到了FOSS的解来达到此目的。通过应用上述方法，本文提出的受控系统可以获得更快的响应和更高的控制精度。最后，为了显示上述方案的优越性和有效性，给出了系留卫星系统和数值结果。