中文摘要：

针对高超声速飞行器模型高度非线性、强耦合的特点,提出了一种多胞形线性变参数系统（LinearParameter Varying,LPV）变增益状态反馈H∞控制器的设计方法。首先在感兴趣的变参数轨迹上选取若干个平衡点进行雅克比线性化并拟合得到LPV模型,将其离散化后存储于一张量中,然后利用高阶奇异值分解（HigherOrder Singular Value Decomposition,HOSVD）,舍去较小和等于0的奇异值及对应的特征向量对其进行降秩重构处理,得到了有限个LTI多胞顶点系统。在对各顶点进行状态反馈控制器设计时,为降低保守性,通过引入松弛变量,将Lyapunov函数矩阵与系统矩阵解耦,从而可以在不同的点使用不同的Lyapunov函数矩阵,以此得到依赖变参数进行增益在线调节的控制器。最后的仿真结果表明了所设计的控制器能够使系统较快地跟踪指令信号,并具有一定的鲁棒性能。

英文摘要：

Considering strong coupling and nonlinearity of the hypersonic vehicle model,a variable gain state feedback H∞ robust controller design methodology based on polytopic LPV system is proposed.Firstly,Jacobian linearization is used on several balance points choose in the trajectory of the scheduling parameters to get the LPV models,then discretizing the system matrix and storing into a tensor,discarding smaller and zero singular values and their corresponding singular vectors though HOSVD,reconstructing the reduced-rank tensor to obtain a finite number of LTI polytopic vertex systems.To reduce the conservatism,a slack variable is inducted into the state feedback controller design for each vertex,and the Lyapunov function is made to be decoupled from system matrix,so we can design different Lyapunov function is made to be decoupled matrix on each vertex to get the parameter-dependent controller with gain adjusted on-line.The final simulation results show that the system using controller designed can follow the command signal rapidly and also have the robustness.