Computational complexity of randomized algorithms for solving parameter-dependent linear matrix inequalities

被引：32
|
作者：
Oishi, Y [1 ]
Kimura, H
机构：
[1] Univ Tokyo, Grad Sch Informat Sci & Technol, Dept Math Informat, Bunkyo Ku, Tokyo 1138656, Japan
[2] Univ Tokyo, Grad Sch Frontier Sci, Dept Complex Sci & Engn, Bunkyo Ku, Tokyo 1130033, Japan
来源：
AUTOMATICA | 2003年 / 39卷 / 12期
关键词：
randomized algorithms; parameter-dependent linear matrix inequalities; computational complexity; conservatism; curse of dimensionality; linear parameter-varying systems;
D O I：
10.1016/j.automatica.2003.07.001
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Randomized algorithms are proposed for solving parameter-dependent linear matrix inequalities and their computational complexity is analyzed. The first proposed algorithm is an adaptation of the algorithms of Polyak and Tempo [(Syst. Control Lett. 43(5) (2001) 343)] and Calafiore and Polyak [(IEEE Trans. Autom. Control 46 (11) (2001) 1755)] for the present problem. It is possible however to show that the expected number of iterations necessary to have a deterministic solution is infinite. In order to make this number finite, the improved algorithm is proposed. The number of iterations necessary to have a probabilistic solution is also considered and is shown to be independent of the parameter dimension. A numerical example is provided. (C) 2003 Elsevier Ltd. All rights reserved.
引用
收藏
页码：2149 / 2156
页数：8
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