Calculation of the structured singular value with gradient-basedoptimization algorithms on a Lie group of structured unitary matrices

Dehaene J.; Cheng Yi; de Moor B.

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Calculation of the structured singular value with gradient-basedoptimization algorithms on a Lie group of structured unitary matrices

机译：Lie组结构unit矩阵的基于梯度的优化算法计算结构奇异值

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The structured singular value problem, which is a basic problem in robustness analysis and design of multivariable controllers, can be formulated as an optimization problem over the manifold of unitary matrices with a given structure. We show how geometric optimization methods, such as the steepest ascent method and the conjugate gradient method for optimization on a Riemannian manifold, lead to algorithms giving a guaranteed nontrivial lower bound for the structured singular value

机译：结构奇异值问题是多变量控制器的鲁棒性分析和设计中的基本问题，可以用给定结构的of矩阵流形上的优化问题来表示。我们展示了几何优化方法（例如最陡峭上升方法和共轭梯度方法）在黎曼流形上的优化如何导致算法给出结构奇异值的有保证的平凡下界

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《IEEE Transactions on Automatic Control》 |1997年第11期|p.1596-1600|共5页
作者
Dehaene J.; Cheng Yi; de Moor B.;
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正文语种 eng
中图分类自动化系统;
关键词
Lie groups; conjugate gradient methods; control system analysis; control system synthesis; matrix algebra; multivariable control systems; optimisation; robust control; singular value decomposition; Lie group; Riemannian manifold; conjugate gradient method; geometric;

机译：李群;共轭梯度法;控制系统分析;控制系统综合;矩阵代数;多变量控制系统;优化;鲁棒控制;奇异值分解;李群;黎曼流形;共轭梯度法;几何;

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机译：Lie组结构unit矩阵上基于梯度的优化算法计算结构奇异值
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Calculation of the structured singular value with gradient-basedoptimization algorithms on a Lie group of structured unitary matrices

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