Model reduction in H2 using matrix solutions of polynomial equations
Model reduction in H2 using matrix solutions of polynomial equations
复制标题
使用多项式方程的矩阵解对 H2 进行模型简化
DOI：
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发表时间：
1998
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通讯作者：
C. T. Chou
中科院分区：
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作者：
B. Hanzon;J. Maciejowski;C. T. Chou
给出了求解SISO线性时不变稳定系统的最优H2近似问题的方法。该方法保证找到全局最优值。它基于构造性代数，但与早期结果相比，该方法对时间和内存的要求要小得多，因此可以应用于麦克米伦度明显更高的系统。通过以特殊形式编写一阶最优条件来避免使用布赫伯格算法，从中可以立即获得格罗布纳基础。通过展示某个空间的有限维基础，将问题转换为线性代数，然后可以通过特征值计算来求解。这种方法有可能更广泛地应用于多项式方程的求解。其中包括两个示例。 *这项研究得到了英国文化协会和荷兰科学基金会 NWO 的支持。这项研究的一部分是在 B.Hanzon 访问剑桥大学工程系时完成的。
A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method guarantees that the global optimum is found. It is based on constructive algebra, but compared with earlier results, the method has much smaller time and memory requirements, and can therefore be applied to systems of significantly higher McMillan degree. The use of Buchberger’s algorithm is avoided by writing the first-order optimality conditions in a special form, from which a Gröbner basis is immediately available. The problem is converted into linear algebra by exhibiting a finite-dimensional basis for a certain space, and can then be solved by eigenvalue calculations. This approach has potential for wider application to the solution of polynomial equations. Two examples are included. ∗This research was supported by the British Council and the Dutch Science Foundation NWO. Part of this research was done while B.Hanzon was visiting Cambridge University Engineering Dept.