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
相关论文
共 50 条
  • [1] Randomized algorithms to solve parameter-dependent linear matrix inequalities and their computational complexity
    Oishi, Y
    Kimura, H
    PROCEEDINGS OF THE 40TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5, 2001, : 2025 - 2030
  • [2] A randomized algorithm for solving parameter-dependent linear matrix inequalities: Computational experience
    Oishi, Y
    SICE 2002: PROCEEDINGS OF THE 41ST SICE ANNUAL CONFERENCE, VOLS 1-5, 2002, : 2561 - 2562
  • [3] A successive constraint approach to solving parameter-dependent linear matrix inequalities
    O'Connor, Robert
    COMPTES RENDUS MATHEMATIQUE, 2017, 355 (06) : 723 - 728
  • [4] Polynomial-time algorithms for probabilistic solutions of parameter-dependent linear matrix inequalities
    Oishi, Yasuaki
    AUTOMATICA, 2007, 43 (03) : 538 - 545
  • [5] Complexity Reduction for Parameter-Dependent Linear Systems
    Farokhi, Farhad
    Sandberg, Henrik
    Johansson, Karl H.
    2013 AMERICAN CONTROL CONFERENCE (ACC), 2013, : 2618 - 2624
  • [6] Existence of homogeneous polynomial solutions for parameter-dependent linear matrix inequalities with parameters in the simplex
    Bliman, P. -A.
    Oliveira, R. C. L. E.
    Montagner, V. F.
    Peres, P. L. D.
    PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, : 1490 - +
  • [7] Stable model reduction for linear variational inequalities with parameter-dependent constraints
    Niakh, Idrissa
    Drouet, Guillaume
    Ehrlacher, Virginie
    Ern, Alexandre
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2023, 57 (01) : 167 - 189
  • [8] Parameter differentiation of linear operators with a parameter-dependent domain
    Lomovtsev, F. E.
    DOKLADY MATHEMATICS, 2012, 86 (01) : 571 - 573
  • [9] RESULTS ABOUT MATRIX ALGORITHMS FOR SOLVING LINEAR AND NONLINEAR ALGEBRAIC INEQUALITIES
    FAZEKAS, F
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1970, 50 (1-4): : T31 - &
  • [10] Parameter differentiation of linear operators with a parameter-dependent domain
    F. E. Lomovtsev
    Doklady Mathematics, 2012, 86 : 571 - 573
12345