Convergence rates of stochastic homogeneous systems

被引：7

作者：

Hoshino, Kenta ^{[1
]}

Nishimura, Yuki ^{[2
]}

Yamashita, Yuh ^{[3
]}

机构：

[1] Aoyama Gakuin Univ, 5-10-1 Fuchinobe, Sagamihara, Kanagawa, Japan

[2] Kagoshima Univ, 1-21-40 Korimoto, Kagoshima, Kagoshima, Japan

[3] Hokkaido Univ, N14W9, Sapporo, Hokkaido, Japan

来源：

SYSTEMS & CONTROL LETTERS | 2019年 / 124卷

基金：

日本学术振兴会;

关键词：

Stochastic control; Finite-time stability; Homogeneous systems; FINITE-TIME STABILITY; STABILIZATION; STABILIZABILITY;

D O I：

10.1016/j.sysconle.2018.11.013

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This study considers stochastic homogeneous systems and focuses on the relation between their homogeneity and the convergence rates. We give a definition of stochastic homogeneous systems with weighted dilations as an extension of deterministic homogeneous systems. We also introduce the stability properties, such as exponential, rational, and finite-time stability with respect to homogeneous norms. As a main result, we show that their homogeneous degrees imply the convergence rates of asymptotically stable systems. Based on the result, we also deal with the stabilization of stochastic homogeneous control systems. We provide a design method of homogeneous feedback laws with homogeneous control Lyapunov functions, which guarantees the convergence rates. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：33 / 39

页数：7

共 50 条

[21] CONVERGENCE RATES AND DECOUPLING IN LINEAR STOCHASTIC APPROXIMATION ALGORITHMS
Kouritzin, Michael A.
Sadeghi, Samira
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2015, 53 (03) : 1484 - 1508
[22] Stochastic approximation algorithms: Nonasymptotic estimation of their convergence rates
Kul'chitskii, OY
Mozgovoi, AE
[J]. AUTOMATION AND REMOTE CONTROL, 1997, 58 (11) : 1817 - 1823
[23] Renewal convergence rates and correlation decay for homogeneous pinning models
Giacomin, Giambattista
[J]. ELECTRONIC JOURNAL OF PROBABILITY, 2008, 13 : 513 - 529
[24] Sharp convergence rates of stochastic approximation for degenerate roots
Fang, HT
Chen, HF
[J]. SCIENCE IN CHINA SERIES E-TECHNOLOGICAL SCIENCES, 1998, 41 (04): : 383 - 392
[25] RATES OF CONVERGENCE FOR STOCHASTIC-APPROXIMATION TYPE ALGORITHMS
KUSHNER, HJ
HUANG, H
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1979, 17 (05) : 607 - 617
[26] Persistence and stochastic convergence of euro area unemployment rates
Kristic, Irena Raguz
Dumancic, Lucija Rogic
Arcabic, Vladimir
[J]. ECONOMIC MODELLING, 2019, 76 : 192 - 198
[27] Stochastic Bernstein polynomials: uniform convergence in probability with rates
Adell, Jose A.
Cardenas-Morales, Daniel
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2020, 46 (02)
[28] Rates of convergence for budget dependent stochastic optimization algorithms
LEcuyer, P
Yin, G
[J]. PROCEEDINGS OF THE 35TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, 1996, : 1069 - 1070
[29] Rates of convergence for a class of global stochastic optimization algorithms
Yin, G
[J]. SIAM JOURNAL ON OPTIMIZATION, 1999, 10 (01) : 99 - 120
[30] Sharp convergence rates of stochastic approximation for degenerate roots
方海涛
陈翰馥
[J]. Science China Technological Sciences, 1998, (04) : 383 - 392

← 1 2 3 4 5 →