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：针对非线性气动弹性系统的阵风载荷减缓问题，本文发展了基于李雅普诺夫稳定性理论的模型参考自适应控制（MRAC）方法。控制器基于由泰勒级数展开与流-固-飞耦合动力学方程的特征向量投影导出的非线性降阶模型构建。给出了完整的MRAC公式化表达，包括编码期望闭环阻尼特性的参考模型设计、具有实时增益调整的自适应控制律，以及保证线性情况下渐近跟踪且非线性残差满足Lipschitz条件时有界跟踪的自适应律李雅普诺夫推导。识别出自适应速率矩阵是最关键的设计参数，它决定了收敛速度、峰值载荷降低与作动器需求之间的权衡关系。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）。针对离散阵风工况，MRAC在相近控制能耗下相比H∞鲁棒控制基准实现了更显著的翼尖偏转降低。在冯·卡门随机湍流作用下，该方法同样获得了有意义的减载效果，且性能随自适应速率的提升而增强。结果表明，MRAC为工作在确定性与随机扰动环境下的柔性飞行器阵风载荷减缓提供了有效框架。