A convex approach to generalized fixed order interpolation

C. Feng; C. M. Lagoa; M. Sznaier

doi:10.1109/acc.2012.6314709

A convex approach to generalized fixed order interpolation

C. Feng, C. M. Lagoa, M. Sznaier

Electrical Engineering

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

3 Scopus citations

Abstract

In this paper, we address the problem of finding a fixed order plant that interpolates given data in time and frequency domain, and satisfies additional constraints such as stability and passivity. The comprehensive framework developed in this paper can be used to address a wide range of complex control problems such as system identification with a priori bound on its order, fixed-order controller design and spectral estimation. To solve the proposed interpolation problem, it is first shown that it can be recast as finding a point in a properly defined semi-algebraic set. Then, an efficient numerical algorithm based on convex relaxations of rank minimization is proposed to solve the problem. Numerical examples are provided to illustrate the efficiency of the algorithm.

Original language	English (US)
Title of host publication	2012 American Control Conference, ACC 2012
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5174-5181
Number of pages	8
ISBN (Print)	9781457710957
DOIs	https://doi.org/10.1109/acc.2012.6314709
State	Published - 2012
Event	2012 American Control Conference, ACC 2012 - Montreal, QC, Canada Duration: Jun 27 2012 → Jun 29 2012

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Other

Other	2012 American Control Conference, ACC 2012
Country/Territory	Canada
City	Montreal, QC
Period	6/27/12 → 6/29/12

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Access to Document

10.1109/acc.2012.6314709

Cite this

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title = "A convex approach to generalized fixed order interpolation",

abstract = "In this paper, we address the problem of finding a fixed order plant that interpolates given data in time and frequency domain, and satisfies additional constraints such as stability and passivity. The comprehensive framework developed in this paper can be used to address a wide range of complex control problems such as system identification with a priori bound on its order, fixed-order controller design and spectral estimation. To solve the proposed interpolation problem, it is first shown that it can be recast as finding a point in a properly defined semi-algebraic set. Then, an efficient numerical algorithm based on convex relaxations of rank minimization is proposed to solve the problem. Numerical examples are provided to illustrate the efficiency of the algorithm.",

author = "C. Feng and Lagoa, {C. M.} and M. Sznaier",

year = "2012",

doi = "10.1109/acc.2012.6314709",

language = "English (US)",

isbn = "9781457710957",

series = "Proceedings of the American Control Conference",

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

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note = "2012 American Control Conference, ACC 2012 ; Conference date: 27-06-2012 Through 29-06-2012",

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Feng, C, Lagoa, CM & Sznaier, M 2012, A convex approach to generalized fixed order interpolation. in 2012 American Control Conference, ACC 2012., 6314709, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 5174-5181, 2012 American Control Conference, ACC 2012, Montreal, QC, Canada, 6/27/12. https://doi.org/10.1109/acc.2012.6314709

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T1 - A convex approach to generalized fixed order interpolation

AU - Feng, C.

AU - Lagoa, C. M.

AU - Sznaier, M.

PY - 2012

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N2 - In this paper, we address the problem of finding a fixed order plant that interpolates given data in time and frequency domain, and satisfies additional constraints such as stability and passivity. The comprehensive framework developed in this paper can be used to address a wide range of complex control problems such as system identification with a priori bound on its order, fixed-order controller design and spectral estimation. To solve the proposed interpolation problem, it is first shown that it can be recast as finding a point in a properly defined semi-algebraic set. Then, an efficient numerical algorithm based on convex relaxations of rank minimization is proposed to solve the problem. Numerical examples are provided to illustrate the efficiency of the algorithm.

AB - In this paper, we address the problem of finding a fixed order plant that interpolates given data in time and frequency domain, and satisfies additional constraints such as stability and passivity. The comprehensive framework developed in this paper can be used to address a wide range of complex control problems such as system identification with a priori bound on its order, fixed-order controller design and spectral estimation. To solve the proposed interpolation problem, it is first shown that it can be recast as finding a point in a properly defined semi-algebraic set. Then, an efficient numerical algorithm based on convex relaxations of rank minimization is proposed to solve the problem. Numerical examples are provided to illustrate the efficiency of the algorithm.

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T3 - Proceedings of the American Control Conference

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BT - 2012 American Control Conference, ACC 2012

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2012 American Control Conference, ACC 2012

Y2 - 27 June 2012 through 29 June 2012

ER -

A convex approach to generalized fixed order interpolation

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