Model Reference Adaptive Control based on Lyapunov stability theory is developed for gust load alleviation of nonlinear aeroelastic systems. The controller operates on a nonlinear reduced-order model derived from Taylor series expansion and eigenvector projection of the coupled fluid-structure-flight dynamic equations. The complete MRAC formulation is presented, including the reference model design that encodes desired closed-loop damping characteristics, the adaptive control law with real-time gain adjustment, and the Lyapunov derivation of the adaptation law that guarantees asymptotic tracking in the linear case and bounded tracking under a Lipschitz condition on the nonlinear residual. The adaptation rate matrix is identified as the single most important design parameter, governing the trade-off between convergence speed, peak load reduction, and actuator demand. Two test cases are considered, a 3DOF aerofoil with cubic stiffness nonlinearities, and a Global Hawk type unmanned aerial vehicle. For the UAV under a discrete gusts, MRAC achieves significant wing-tip deflection reductions, outperforming the H infinity robust control benchmark with comparable control effort. Under Von Karman stochastic turbulence, meaningful reductions are also obtained, with performance scaling with the adaptation rate. The results demonstrate that MRAC provides an effective framework for GLA of flexible aircraft operating in both deterministic and stochastic disturbance environments.

翻译：本文基于Lyapunov稳定性理论，发展了用于非线性气动弹性系统阵风减缓的模型参考自适应控制（MRAC）。该控制器作用于由Taylor级数展开与耦合流-固-飞行力学方程特征向量投影导出的非线性降阶模型。文章给出了完整的MRAC公式体系，包括编码期望闭环阻尼特性的参考模型设计、带实时增益调整的自适应控制律，以及保证线性情形下渐近跟踪、非线性残差满足Lipschitz条件时有界跟踪的自适应律Lyapunov推导过程。自适应速率矩阵被识别为唯一最重要的设计参数，它主导着收敛速度、峰值载荷降低与作动器需求之间的权衡。研究考虑了两个测试案例：具有三次刚度非线性的三自由度（3DOF）翼型，以及"全球鹰"型无人机（UAV）。对于离散阵风作用下的UAV，MRAC实现了显著的翼尖挠度减小，在以相当控制力度的比较中优于H∞鲁棒控制基准。在Von Karman随机湍流条件下，MRAC也获得了有意义的载荷降低效果，且性能随自适应速率增大而提升。结果表明，MRAC为运行于确定性与随机扰动环境中的柔性飞机提供了有效的阵风减缓（GLA）框架。