Stability of drinking water distribution network

Tobias Leth; Carsten Skovmose Kallesøe; Christoffer Sloth; Rafał Wisniewski

doi:10.1109/ECC.2016.7810546

Stability of drinking water distribution network

Tobias Leth, Carsten Skovmose Kallesøe, Christoffer Sloth, Rafał Wisniewski

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

We strive to prove stability of a hydraulic network, where the pressure at the end user is controlled with PI control. The non-polynomial model is represented by numerous polynomial systems defined on sub-sets of Rⁿ. The sub-sets are defined by compact basic semi-algebraic sets. The stability of the PI-controller is proved by designing a Lyapunov function which fulfils different criteria in different sub-sets of Rⁿ. We find a polynomial Lyapunov function for the system using SOSTOOLS supported by Putinar's Positivstellensatz.

Original language	English
Title of host publication	2016 European Control Conference, ECC 2016
Number of pages	6
Publisher	IEEE
Publication date	6. Jan 2016
Pages	1764-1769
Article number	7810546
ISBN (Electronic)	9781509025916
DOIs	https://doi.org/10.1109/ECC.2016.7810546
Publication status	Published - 6. Jan 2016
Externally published	Yes
Event	2016 European Control Conference, ECC 2016 - Aalborg, Denmark Duration: 29. Jun 2016 → 1. Jul 2016

Conference

Conference	2016 European Control Conference, ECC 2016
Country/Territory	Denmark
City	Aalborg
Period	29/06/2016 → 01/07/2016

Documents & Links

10.1109/ECC.2016.7810546

Cite this

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title = "Stability of drinking water distribution network",

abstract = "We strive to prove stability of a hydraulic network, where the pressure at the end user is controlled with PI control. The non-polynomial model is represented by numerous polynomial systems defined on sub-sets of Rn. The sub-sets are defined by compact basic semi-algebraic sets. The stability of the PI-controller is proved by designing a Lyapunov function which fulfils different criteria in different sub-sets of Rn. We find a polynomial Lyapunov function for the system using SOSTOOLS supported by Putinar's Positivstellensatz.",

author = "Tobias Leth and Kalles{\o}e, {Carsten Skovmose} and Christoffer Sloth and Rafa{\l} Wisniewski",

year = "2016",

month = jan,

day = "6",

doi = "10.1109/ECC.2016.7810546",

language = "English",

pages = "1764--1769",

booktitle = "2016 European Control Conference, ECC 2016",

publisher = "IEEE",

address = "United States",

note = "2016 European Control Conference, ECC 2016 ; Conference date: 29-06-2016 Through 01-07-2016",

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TY - GEN

T1 - Stability of drinking water distribution network

AU - Leth, Tobias

AU - Kallesøe, Carsten Skovmose

AU - Sloth, Christoffer

AU - Wisniewski, Rafał

PY - 2016/1/6

Y1 - 2016/1/6

N2 - We strive to prove stability of a hydraulic network, where the pressure at the end user is controlled with PI control. The non-polynomial model is represented by numerous polynomial systems defined on sub-sets of Rn. The sub-sets are defined by compact basic semi-algebraic sets. The stability of the PI-controller is proved by designing a Lyapunov function which fulfils different criteria in different sub-sets of Rn. We find a polynomial Lyapunov function for the system using SOSTOOLS supported by Putinar's Positivstellensatz.

AB - We strive to prove stability of a hydraulic network, where the pressure at the end user is controlled with PI control. The non-polynomial model is represented by numerous polynomial systems defined on sub-sets of Rn. The sub-sets are defined by compact basic semi-algebraic sets. The stability of the PI-controller is proved by designing a Lyapunov function which fulfils different criteria in different sub-sets of Rn. We find a polynomial Lyapunov function for the system using SOSTOOLS supported by Putinar's Positivstellensatz.

U2 - 10.1109/ECC.2016.7810546

DO - 10.1109/ECC.2016.7810546

M3 - Article in proceedings

AN - SCOPUS:85015019768

SP - 1764

EP - 1769

BT - 2016 European Control Conference, ECC 2016

PB - IEEE

T2 - 2016 European Control Conference, ECC 2016

Y2 - 29 June 2016 through 1 July 2016

ER -

Stability of drinking water distribution network

Abstract

Conference

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Cite this