ABSTRACT This paper addresses the fault-tolerant control issue for a class of flexible air-breathing hypersonic vehicles. Firstly, a longitudinal dynamic model with process faults is established, which contains an ordinary differential equation (ODE) for rigid body, an Euler–Bernoulli beam equation for flexible modes, and a new boundary connection between them; Secondly, a novel fault-tolerant control scheme is proposed to accommodate process faults and suppress vibrations, which relies on the direct Lyapunov method and the bilinear matrix inequalities (BMIs) technique; Thirdly, in order to compute the gain matrices of the fault-tolerant control law, a two-step algorithm is provided to solve the BMI feasibility problem in terms of linear matrix inequality optimisation technique. Finally, the simulation results are provided to illustrate the effectiveness of the theoretical results.

中文翻译：

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线性常微分方程系统中柔性吸气式高超声速飞行器的容错控制

摘要 本文解决了一类柔性吸气式高超声速飞行器的容错控制问题。首先，建立了具有过程故障的纵向动力学模型，该模型包含刚体常微分方程（ODE）、柔性模态的欧拉-伯努利梁方程以及它们之间的新边界连接；其次，基于直接李雅普诺夫方法和双线性矩阵不等式（BMI）技术，提出了一种新的容错控制方案来适应过程故障和抑制振动；第三，为了计算容错控制律的增益矩阵，提出了一种两步算法来解决基于线性矩阵不等式优化技术的BMI可行性问题。最后，