基于高阶奇异值理论的LPV系统多胞分解  

Polytopic Decomposition of the Linear Parameter-Varying Model based on HOSVD

作　　者：王明昊 刘刚[1] 侯洪庆[1] 杨述华 

机构地区：[1]第二炮兵工程大学701教研室,陕西西安710025 [2]第二炮兵驻211厂军事代表室,北京100076

出　　处：《控制工程》2013年第S1期109-111,116,共4页Control Engineering of China

基　　金：国家自然科学基金重点资助项目(61132008)

摘　　要：针对线性变参数(Linear Parameter Varying,LPV)系统需要在整个变参数的轨迹上求解无穷个LMI的问题,提出了一种利用张量积转换的方法将其转换为凸多胞形结构。首先将给定的变增益LPV系统在变参数的作用区间内对其进行离散化处理并存储于一张量中,然后利用高阶奇异值分解(Higher Order Singular Value Decomposition,HOSVD),舍去较小和为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顶点系统,进而可以针对每个顶点系统设计满足控制系统要求的控制器,最后通过其凸组合得到最终的闭环系统变增益控制器。仿真结果表明该方法获得的多胞系统能够在容许的误差范围内表示原LPV系统且最终得到的控制器能够满足闭环系统设计要求。For the solution of an infinite number of LMI in the parameters trajectory of LPV system,a method based on the tensor product transformation is proposed to transform the LPV system into the convex polytopic structure.Firstly,discrete the given LPV system within the interzone of the changing parameters and storing it into a tensor,and then using HOSVD,discarding smaller and non-zero singular values and their corresponding singular vectors,reconstructing the reduced-rank tensor to obtain a finite number of LTI vertex systems,then,we can design the controller satisfied the request of the closed-loop system for each LTI vertex system.The final controller can be obtained by the convex combination of the vertex.The simulation shows that the convex polytopic system obtained by this method can substitute the original LPV system within the allowed error and also satisfy the goal of control design.

关 键 词：高阶奇异值分解 线性变参数系统 张量 多胞系统 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]