Optimization of the H∞-norm of Dynamic Flow Networks

Alexander Johansson; Jieqiang Wei; Henrik Sandberg; Karl H. Johansson; Jie Chen

doi:10.23919/ACC.2018.8431398

Optimization of the H_∞-norm of Dynamic Flow Networks

Alexander Johansson, Jieqiang Wei^*, Henrik Sandberg, Karl H. Johansson^*, Jie Chen

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

4 Citations (Scopus)

Abstract

In this paper, we study the H_∞- norm of linear systems over graphs, which is used to model distribution networks. In particular, we aim to minimize the H_∞- norm subject to allocation of the weights on the edges. The optimization problem is formulated with LMI (Linear-Matrix-Inequality) constraints. For distribution networks with one port, i.e., SISO systems, we show that the H_∞- norm coincides with the effective resistance between the nodes in the port. Moreover, we derive an upper bound of the H_∞- norm, which is in terms of the algebraic connectivity of the graph on which the distribution network is defined.

Original language	English
Title of host publication	2018 Annual American Control Conference (ACC)
Publisher	IEEE
Pages	1280-1285
ISBN (Electronic)	978-1-5386-5428-6
ISBN (Print)	978-1-5386-5429-3
DOIs	https://doi.org/10.23919/ACC.2018.8431398
Publication status	Published - 2018
Event	1st Annual American Control Conference (ACC 2018) - Wisconsin Center, Milwaukee, United States Duration: 27 Jun 2018 → 29 Jun 2018 http://acc2018.a2c2.org

Publication series

Name	American Control Conference (ACC)
Publisher	IEEE
ISSN (Print)	0743-1619
ISSN (Electronic)	2378-5861

Conference

Conference	1st Annual American Control Conference (ACC 2018)
Place	United States
City	Milwaukee
Period	27/06/18 → 29/06/18
Internet address	http://acc2018.a2c2.org

Research Keywords

SYSTEMS

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10.23919/ACC.2018.8431398

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Cite this

@inproceedings{5ba9d0011fa14eab916a5d405bc90606,

title = "Optimization of the H∞-norm of Dynamic Flow Networks",

abstract = "In this paper, we study the H∞- norm of linear systems over graphs, which is used to model distribution networks. In particular, we aim to minimize the H∞- norm subject to allocation of the weights on the edges. The optimization problem is formulated with LMI (Linear-Matrix-Inequality) constraints. For distribution networks with one port, i.e., SISO systems, we show that the H∞- norm coincides with the effective resistance between the nodes in the port. Moreover, we derive an upper bound of the H∞- norm, which is in terms of the algebraic connectivity of the graph on which the distribution network is defined.",

keywords = "SYSTEMS",

author = "Alexander Johansson and Jieqiang Wei and Henrik Sandberg and Johansson, {Karl H.} and Jie Chen",

year = "2018",

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Johansson, A, Wei, J, Sandberg, H, Johansson, KH & Chen, J 2018, Optimization of the H_∞-norm of Dynamic Flow Networks. in 2018 Annual American Control Conference (ACC)., 8431398, American Control Conference (ACC), IEEE, pp. 1280-1285, 1st Annual American Control Conference (ACC 2018), Milwaukee, Wisconsin, United States, 27/06/18. https://doi.org/10.23919/ACC.2018.8431398

Optimization of the H_∞-norm of Dynamic Flow Networks. / Johansson, Alexander; Wei, Jieqiang; Sandberg, Henrik et al.
2018 Annual American Control Conference (ACC). IEEE, 2018. p. 1280-1285 8431398 (American Control Conference (ACC)).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

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AB - In this paper, we study the H∞- norm of linear systems over graphs, which is used to model distribution networks. In particular, we aim to minimize the H∞- norm subject to allocation of the weights on the edges. The optimization problem is formulated with LMI (Linear-Matrix-Inequality) constraints. For distribution networks with one port, i.e., SISO systems, we show that the H∞- norm coincides with the effective resistance between the nodes in the port. Moreover, we derive an upper bound of the H∞- norm, which is in terms of the algebraic connectivity of the graph on which the distribution network is defined.

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