Asymptotic exactness of parameter-dependent lyapunov functions: An error bound and exactness verification
Asymptotic exactness of parameter-dependent lyapunov functions: An error bound and exactness verification
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DOI：
10.1109/cdc.2007.4434845
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发表时间：
2007-12
期刊：
影响因子：
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通讯作者：
Y. Oishi
中科院分区：
文献类型：
--
作者：
Y. Oishi
本文提供了一种解决带有函数变量的鲁棒半定规划问题的近似方法，并证明了其渐近精确性。该问题涵盖了各种控制问题，包括使用参数相关的李亚普诺夫函数进行鲁棒稳定性/性能分析。在所提出的方法中，基于参数值集的划分构造近似半定规划问题。这种方法是渐近精确的，因为随着除法的分辨率变高，构造的近似问题的最优值收敛到原始问题的最优值。我们的收敛分析是定量的。特别是，本文给出了两个问题最优值之间差异的先验上限。此外，它还讨论了如何验证近似问题的最优解对于原始问题实际上也是最优的。
This paper provides an approximate approach to a robust semidefinite programming problem with a functional variable and shows its asymptotic exactness. This problem covers a variety of control problems including a robust stability/performance analysis with a parameter-dependent Lyapunov function. In the proposed approach, an approximate semidefinite programming problem is constructed based on the division of the set of parameter values. This approach is asymptotically exact in the sense that, as the resolution of the division becomes higher, the optimal value of the constructed approximate problem converges to that of the original problem. Our convergence analysis is quantitative. In particular, this paper gives an a priori upper bound on the discrepancy between the optimal values of the two problems. Moreover, it discusses how to verify that an optimal solution of the approximate problem is actually optimal also for the original problem.