Convex synthesis of symmetric modifications to linear systems

Neil K. Dhingra; Mihailo Jovanovic

doi:10.1109/ACC.2015.7171886

Convex synthesis of symmetric modifications to linear systems

Neil K. Dhingra, Mihailo Jovanovic

Electrical and Computer Engineering

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

8 Scopus citations

Abstract

We develop a method for designing symmetric modifications to linear dynamical systems for the purpose of optimizing H₂ performance. For systems with symmetric dynamic matrices this problem is convex. While in the absence of symmetry the design problem is not convex in general, we show that the H₂ norm of the symmetric part of the system provides an upper bound on the H₂ norm of the original system. We then study the particular case where the modifications are given by a weighted sum of diagonal matrices and develop an efficient customized algorithm for computing the optimal solution. Finally, we illustrate the efficacy of our approach on a combination drug therapy example for HIV treatment.

Original language	English (US)
Title of host publication	ACC 2015 - 2015 American Control Conference
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3583-3588
Number of pages	6
ISBN (Electronic)	9781479986842
DOIs	https://doi.org/10.1109/ACC.2015.7171886
State	Published - Jul 28 2015
Event	2015 American Control Conference, ACC 2015 - Chicago, United States Duration: Jul 1 2015 → Jul 3 2015

Publication series

Name	Proceedings of the American Control Conference
Volume	2015-July
ISSN (Print)	0743-1619

Conference

Conference	2015 American Control Conference, ACC 2015
Country/Territory	United States
City	Chicago
Period	7/1/15 → 7/3/15

Bibliographical note

Publisher Copyright:
© 2015 American Automatic Control Council.

Keywords

combination drug therapy
networks
sparse controller synthesis
structured design
symmetric systems

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1109/ACC.2015.7171886

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Convex synthesis of symmetric modifications to linear systems. / Dhingra, Neil K.; Jovanovic, Mihailo.

ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2015. p. 3583-3588 7171886 (Proceedings of the American Control Conference; Vol. 2015-July).

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

Dhingra, NK & Jovanovic, M 2015, Convex synthesis of symmetric modifications to linear systems. in ACC 2015 - 2015 American Control Conference., 7171886, Proceedings of the American Control Conference, vol. 2015-July, Institute of Electrical and Electronics Engineers Inc., pp. 3583-3588, 2015 American Control Conference, ACC 2015, Chicago, United States, 7/1/15. https://doi.org/10.1109/ACC.2015.7171886

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abstract = "We develop a method for designing symmetric modifications to linear dynamical systems for the purpose of optimizing H2 performance. For systems with symmetric dynamic matrices this problem is convex. While in the absence of symmetry the design problem is not convex in general, we show that the H2 norm of the symmetric part of the system provides an upper bound on the H2 norm of the original system. We then study the particular case where the modifications are given by a weighted sum of diagonal matrices and develop an efficient customized algorithm for computing the optimal solution. Finally, we illustrate the efficacy of our approach on a combination drug therapy example for HIV treatment.",

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AB - We develop a method for designing symmetric modifications to linear dynamical systems for the purpose of optimizing H2 performance. For systems with symmetric dynamic matrices this problem is convex. While in the absence of symmetry the design problem is not convex in general, we show that the H2 norm of the symmetric part of the system provides an upper bound on the H2 norm of the original system. We then study the particular case where the modifications are given by a weighted sum of diagonal matrices and develop an efficient customized algorithm for computing the optimal solution. Finally, we illustrate the efficacy of our approach on a combination drug therapy example for HIV treatment.

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KW - networks

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Convex synthesis of symmetric modifications to linear systems

Abstract

Publication series

Conference

Bibliographical note

Keywords

UN SDGs

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