Krasovskii's Method in the Stability of Network Control

被引：11

作者：

Feijer, Diego ^{[1
]}

Paganini, Fernando ^{[1
]}

机构：

[1] Univ ORT Uruguay, Dept Elect Engn, Montevideo 11100, Uruguay

来源：

2009 AMERICAN CONTROL CONFERENCE, VOLS 1-9 | 2009年

关键词：

OPTIMIZATION;

D O I：

10.1109/ACC.2009.5160529

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider network resource allocation problems based on convex optimization, and their decentralized solutions by means of primal, dual, or primal-dual subgradient control. We show how Krasovskii's method, that seeks Lyapunov functions which are quadratic forms of the vector field, provides new global stability proofs for various problems of this kind. Applications include congestion control, cross-layer congestion and contention control, and other general network utility maximization problems. We show more generally how this proof method applies to concave-convex saddle point problems solved by subgradient methods.

引用

页码：3292 / 3297

页数：6

共 17 条

[1]

Arrow K. J., 1958, Stanford Mathematical Studies in the Social Sciences

[2] Multiple Lyapunov functions and other analysis tools for switched and hybrid systems [J].

Branicky, MS .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1998, 43 (04) :475-482

[3] Layering as optimization decomposition: A mathematical theory of network architectures [J].

Chiang, Mung ;

Low, Steven H. ;

Calderbank, A. Robert ;

Doyle, John C. .

PROCEEDINGS OF THE IEEE, 2007, 95 (01) :255-312

[4] Rate control for communication networks: shadow prices, proportional fairness and stability [J].

Kelly, FP ;

Maulloo, AK ;

Tan, DKH .

JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY, 1998, 49 (03) :237-252

[5]

Khalil H. K., 2002, Nonlinear systems, V3

[6]

Krasovskii N., 1963, Problems of the theory of stability of motion

[7] Utility-optimal random-access control [J].

Lee, Jang-Won ;

Chiang, Mung ;

Calderbank, A. Robert .

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, 2007, 6 (07) :2741-2751

[8] Jointly optimal congestion and contention control based on network utility maximization [J].

Lee, Jang-Won ;

Chiang, Mung ;

Calderbank, A. Robert .

IEEE COMMUNICATIONS LETTERS, 2006, 10 (03) :216-218

[9] A tutorial on cross-layer optimization in wireless networks [J].

Lin, Xiaojun ;

Shroff, Ness B. ;

Srikant, R. .

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, 2006, 24 (08) :1452-1463

[10] Optimization flow control - I: Basic algorithm and convergence [J].

Low, SH ;

Lapsley, DE .

IEEE-ACM TRANSACTIONS ON NETWORKING, 1999, 7 (06) :861-874

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