Time-varying control laws with guaranteed persistence for a class of multi-species chemostats

Frédéric Mazenc; Zhong Ping Jiang

doi:10.1109/CDC.2009.5399908

Time-varying control laws with guaranteed persistence for a class of multi-species chemostats

Frédéric Mazenc, Zhong Ping Jiang

Electrical and Computer Engineering

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

Abstract

We study classical families of chemostat models with an arbitrary number of species competing for a single limiting substrate. For families of models, we present some obstructions to the existence of asymptotically stabilizable periodic trajectories. For other families of growth rates, we design a dilution rate and input substrate time-varying feedback controllers so that a positive trajectory of the chemostat model becomes globally asymptotically stable. That way, the control laws ensure persistence of all the species. A local version of this result is given in the case where only the substrate concentration is available by measurement.

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	7710-7715
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5399908
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

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2009.5399908

Cite this

Mazenc, F., & Jiang, Z. P. (2009). Time-varying control laws with guaranteed persistence for a class of multi-species chemostats. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 7710-7715). Article 5399908 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5399908

Time-varying control laws with guaranteed persistence for a class of multi-species chemostats. / Mazenc, Frédéric; Jiang, Zhong Ping.
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. 7710-7715 5399908 (Proceedings of the IEEE Conference on Decision and Control).

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

Mazenc, F & Jiang, ZP 2009, Time-varying control laws with guaranteed persistence for a class of multi-species chemostats. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5399908, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 7710-7715, 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.2009.5399908

Mazenc F, Jiang ZP. Time-varying control laws with guaranteed persistence for a class of multi-species chemostats. 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. 7710-7715. 5399908. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5399908

Mazenc, Frédéric ; Jiang, Zhong Ping. / Time-varying control laws with guaranteed persistence for a class of multi-species chemostats. 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. 7710-7715 (Proceedings of the IEEE Conference on Decision and Control).

@inproceedings{fdfa626ee408495d879ae0d2853b8ba4,

title = "Time-varying control laws with guaranteed persistence for a class of multi-species chemostats",

abstract = "We study classical families of chemostat models with an arbitrary number of species competing for a single limiting substrate. For families of models, we present some obstructions to the existence of asymptotically stabilizable periodic trajectories. For other families of growth rates, we design a dilution rate and input substrate time-varying feedback controllers so that a positive trajectory of the chemostat model becomes globally asymptotically stable. That way, the control laws ensure persistence of all the species. A local version of this result is given in the case where only the substrate concentration is available by measurement.",

author = "Fr{\'e}d{\'e}ric Mazenc and Jiang, {Zhong Ping}",

year = "2009",

doi = "10.1109/CDC.2009.5399908",

language = "English (US)",

isbn = "9781424438716",

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

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

pages = "7710--7715",

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

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",

}

TY - GEN

T1 - Time-varying control laws with guaranteed persistence for a class of multi-species chemostats

AU - Mazenc, Frédéric

AU - Jiang, Zhong Ping

PY - 2009

Y1 - 2009

N2 - We study classical families of chemostat models with an arbitrary number of species competing for a single limiting substrate. For families of models, we present some obstructions to the existence of asymptotically stabilizable periodic trajectories. For other families of growth rates, we design a dilution rate and input substrate time-varying feedback controllers so that a positive trajectory of the chemostat model becomes globally asymptotically stable. That way, the control laws ensure persistence of all the species. A local version of this result is given in the case where only the substrate concentration is available by measurement.

AB - We study classical families of chemostat models with an arbitrary number of species competing for a single limiting substrate. For families of models, we present some obstructions to the existence of asymptotically stabilizable periodic trajectories. For other families of growth rates, we design a dilution rate and input substrate time-varying feedback controllers so that a positive trajectory of the chemostat model becomes globally asymptotically stable. That way, the control laws ensure persistence of all the species. A local version of this result is given in the case where only the substrate concentration is available by measurement.

UR - http://www.scopus.com/inward/record.url?scp=77950806090&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950806090&partnerID=8YFLogxK

U2 - 10.1109/CDC.2009.5399908

DO - 10.1109/CDC.2009.5399908

M3 - Conference contribution

AN - SCOPUS:77950806090

SN - 9781424438716

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 7710

EP - 7715

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.

T2 - 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

Y2 - 15 December 2009 through 18 December 2009

ER -

Time-varying control laws with guaranteed persistence for a class of multi-species chemostats

Abstract

Publication series

Other

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this