Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities
Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities
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DOI：
10.1080/00207179.2010.531397
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发表时间：
2010-01
影响因子：
2.1
通讯作者：
J. Rauch;Xu Zhang;E. Zuazua
中科院分区：
文献类型：
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作者：
J. Rauch;Xu Zhang;E. Zuazua
使用Hermite的多项式稳定性条件的制定，静态输出反馈（SOF）控制器的设计可以制定为一个多项式矩阵不等式（PMI），一个（一般非凸）非线性半定规划问题，可以解决（局部）与PENNON，一个实施的惩罚和增广拉格朗日方法。通常情况下，Hermite SOF PMI问题的规模很大，实验表明，这对求解器的整体性能有负面影响。在这份说明中，我们回顾代数解释厄米的二次型作为一个特定的Bézoutian和我们使用的结果多项式插值表示厄米PMI在拉格朗日多项式的基础上，作为替代传统的权力基础。基准问题的数值实验表明，该方法带来的改善，在问题的缩放，迭代次数和收敛行为的PENNON。
Using Hermite's formulation of polynomial stability conditions, static output feedback (SOF) controller design can be formulated as a polynomial matrix inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming problem that can be solved (locally) with PENNON, an implementation of a penalty and augmented Lagrangian method. Typically, Hermite SOF PMI problems are badly scaled and experiments reveal that this has a negative impact on the overall performance of the solver. In this note we recall the algebraic interpretation of Hermite's quadratic form as a particular Bézoutian and we use results on polynomial interpolation to express the Hermite PMI in a Lagrange polynomial basis, as an alternative to the conventional power basis. Numerical experiments on benchmark problem instances show the improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behaviour of PENNON.