Distributional robustness analysis for polynomial uncertainty

Chao Feng; Constantino M. Lagoa

doi:10.1109/CDC.2009.5399737

Distributional robustness analysis for polynomial uncertainty

Chao Feng, Constantino M. Lagoa

Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Scopus citations

Abstract

This paper addresses the problem of computing the worst-case expected value of a polynomial function, over a class of admissible distributions. It is shown that this problem, for the class of distributions considered, is equivalent to a convex optimization problem for which efficient linear matrix inequality (LMI) relaxations are available. In case that the performance function is continuous (not necessarily polynomial), the worst-case expected value can be approximated by using its polynomial approximations. Moreover, the proposed approach is applied to compute hard bounds of the worst-case probability of a polynomial being negative. Numerical examples are presented which illustrate the application of the results in this paper.

Original language	English (US)
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1151-1156
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5399737
State	Published - 2009
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: Dec 15 2009 → Dec 18 2009

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	12/15/09 → 12/18/09

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2009.5399737

Cite this

Feng, C., & Lagoa, C. M. (2009). Distributional robustness analysis for polynomial uncertainty. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 1151-1156). Article 5399737 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5399737

Feng, Chao ; Lagoa, Constantino M. / Distributional robustness analysis for polynomial uncertainty. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. pp. 1151-1156 (Proceedings of the IEEE Conference on Decision and Control).

@inproceedings{23bd588596764f9caae06f1fef50b0ca,

title = "Distributional robustness analysis for polynomial uncertainty",

abstract = "This paper addresses the problem of computing the worst-case expected value of a polynomial function, over a class of admissible distributions. It is shown that this problem, for the class of distributions considered, is equivalent to a convex optimization problem for which efficient linear matrix inequality (LMI) relaxations are available. In case that the performance function is continuous (not necessarily polynomial), the worst-case expected value can be approximated by using its polynomial approximations. Moreover, the proposed approach is applied to compute hard bounds of the worst-case probability of a polynomial being negative. Numerical examples are presented which illustrate the application of the results in this paper.",

author = "Chao Feng and Lagoa, {Constantino M.}",

year = "2009",

doi = "10.1109/CDC.2009.5399737",

language = "English (US)",

isbn = "9781424438716",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "1151--1156",

booktitle = "Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009",

address = "United States",

note = "48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 ; Conference date: 15-12-2009 Through 18-12-2009",

}

Feng, C & Lagoa, CM 2009, Distributional robustness analysis for polynomial uncertainty. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5399737, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 1151-1156, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 12/15/09. https://doi.org/10.1109/CDC.2009.5399737

Distributional robustness analysis for polynomial uncertainty. / Feng, Chao; Lagoa, Constantino M.
Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 1151-1156 5399737 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Lagoa, Constantino M.

PY - 2009

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N2 - This paper addresses the problem of computing the worst-case expected value of a polynomial function, over a class of admissible distributions. It is shown that this problem, for the class of distributions considered, is equivalent to a convex optimization problem for which efficient linear matrix inequality (LMI) relaxations are available. In case that the performance function is continuous (not necessarily polynomial), the worst-case expected value can be approximated by using its polynomial approximations. Moreover, the proposed approach is applied to compute hard bounds of the worst-case probability of a polynomial being negative. Numerical examples are presented which illustrate the application of the results in this paper.

AB - This paper addresses the problem of computing the worst-case expected value of a polynomial function, over a class of admissible distributions. It is shown that this problem, for the class of distributions considered, is equivalent to a convex optimization problem for which efficient linear matrix inequality (LMI) relaxations are available. In case that the performance function is continuous (not necessarily polynomial), the worst-case expected value can be approximated by using its polynomial approximations. Moreover, the proposed approach is applied to compute hard bounds of the worst-case probability of a polynomial being negative. Numerical examples are presented which illustrate the application of the results in this paper.

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DO - 10.1109/CDC.2009.5399737

M3 - Conference contribution

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T3 - Proceedings of the IEEE Conference on Decision and Control

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EP - 1156

BT - Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

PB - Institute of Electrical and Electronics Engineers Inc.

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Feng C, Lagoa CM. Distributional robustness analysis for polynomial uncertainty. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 1151-1156. 5399737. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5399737

Distributional robustness analysis for polynomial uncertainty

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