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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 Linear Variable Varying (LPV) system, an infinite number of LMIs need to be solved on the trajectory of the variable parameters. A transformation method using tensor product is proposed to convert it into convex polygon structure. Firstly, a given variable gain LPV system is discretized and stored in a range of variables within the range of variable parameters, and then using the Higher Order Singular Value Decomposition (HOSVD), the smaller and the smaller A singular value of 0 and its corresponding eigenvector. Then, a reduced-rank reconstruction process is performed to obtain a finite number of LTI vertex systems. Then, a controller satisfying the requirements of the control system can be designed for each vertex system. Finally, The final closed-loop system gain controller. The simulation results show that the multi-cell system obtained by this method can represent the original LPV system within the allowable error range and the resulting controller can meet the design requirements of the closed-loop system.