The Modified Optimal Hinfinity Control Problem for Descriptor Systems
The Modified Optimal Hinfinity Control Problem for Descriptor Systems
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描述符系统的改进最优Hinfinity控制问题
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Timo Reis
中科院分区：
文献类型：
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作者：
Philip Losse;V. Mehrmann;L. Poppe;Timo Reis
研究了线性常系数广义系统的数学H_∞控制问题.对于任意指标的系统，得到了最优性的充分必要条件。这些条件制定在紧缩子空间的甚至矩阵铅笔只包含原系统的参数。结果表明，这种方法导致一个更强大的数值和有效的方法，在计算最佳值$伽玛$相比，其他方法，如广泛使用的Riccati和线性矩阵不等式（LMI）为基础的方法。最后通过数值算例说明了结果。
The $mathcal{H}_infty$ control problem is studied for linear constant coefficient descriptor systems. Necessary and sufficient optimality conditions are derived for systems of arbitrary index. These conditions are formulated in terms of deflating subspaces of even matrix pencils containing only the parameters of the original system. It is shown that this approach leads to a more numerically robust and efficient method in computing the optimal value $gamma$ in contrast to other methods such as the widely used Riccati- and linear matrix inequality (LMI)-based approaches. The results are illustrated by a numerical example.