Spatial controllability and multiple actuator placement for dissipative partial differential equation systems

Antonios Armaou, Michael A. Demetriou

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

1 Citation (Scopus)

Abstract

This manuscript considers the problem of actuator placement for transport-reaction processes, which are mathematically modelled by linear parabolic partial differential equations. The novelty of the proposed optimization scheme is that it considers the controllability of specific modes while at the same time minimizes the spillover effects due to intermediate range modes. Using modal decomposition for space discretization, along with the notions of spatial and modal controllabilities, the semi-infinite optimization problem is formulated as a nonlinear optimization problem in appropriate L? spaces. To address the problem of actuator clusterization, a modification to earlier efforts is introduced, which takes the form of an additional constraint in the location optimization. The formulated optimization problem is subsequently solved using standard search algorithms. The proposed method is successfully applied to a representative process, modelled by a one-dimensional parabolic PDE, where the optimal location of multiple actuators is computed.

Original languageEnglish (US)
Title of host publicationProceedings of the 2006 American Control Conference
Pages1473-1480
Number of pages8
StatePublished - Dec 1 2006
Event2006 American Control Conference - Minneapolis, MN, United States
Duration: Jun 14 2006 → Jun 16 2006

Publication series

NameProceedings of the American Control Conference
Volume2006
ISSN (Print)0743-1619

Other

Other2006 American Control Conference
CountryUnited States
CityMinneapolis, MN
Period6/14/06 → 6/16/06

Fingerprint

Controllability
Partial differential equations
Actuators
Decomposition

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Armaou, A., & Demetriou, M. A. (2006). Spatial controllability and multiple actuator placement for dissipative partial differential equation systems. In Proceedings of the 2006 American Control Conference (pp. 1473-1480). [1656426] (Proceedings of the American Control Conference; Vol. 2006).
Armaou, Antonios ; Demetriou, Michael A. / Spatial controllability and multiple actuator placement for dissipative partial differential equation systems. Proceedings of the 2006 American Control Conference. 2006. pp. 1473-1480 (Proceedings of the American Control Conference).
@inproceedings{fcd7f81108fa41018837284985277442,
title = "Spatial controllability and multiple actuator placement for dissipative partial differential equation systems",
abstract = "This manuscript considers the problem of actuator placement for transport-reaction processes, which are mathematically modelled by linear parabolic partial differential equations. The novelty of the proposed optimization scheme is that it considers the controllability of specific modes while at the same time minimizes the spillover effects due to intermediate range modes. Using modal decomposition for space discretization, along with the notions of spatial and modal controllabilities, the semi-infinite optimization problem is formulated as a nonlinear optimization problem in appropriate L? spaces. To address the problem of actuator clusterization, a modification to earlier efforts is introduced, which takes the form of an additional constraint in the location optimization. The formulated optimization problem is subsequently solved using standard search algorithms. The proposed method is successfully applied to a representative process, modelled by a one-dimensional parabolic PDE, where the optimal location of multiple actuators is computed.",
author = "Antonios Armaou and Demetriou, {Michael A.}",
year = "2006",
month = "12",
day = "1",
language = "English (US)",
isbn = "1424402107",
series = "Proceedings of the American Control Conference",
pages = "1473--1480",
booktitle = "Proceedings of the 2006 American Control Conference",

}

Armaou, A & Demetriou, MA 2006, Spatial controllability and multiple actuator placement for dissipative partial differential equation systems. in Proceedings of the 2006 American Control Conference., 1656426, Proceedings of the American Control Conference, vol. 2006, pp. 1473-1480, 2006 American Control Conference, Minneapolis, MN, United States, 6/14/06.

Spatial controllability and multiple actuator placement for dissipative partial differential equation systems. / Armaou, Antonios; Demetriou, Michael A.

Proceedings of the 2006 American Control Conference. 2006. p. 1473-1480 1656426 (Proceedings of the American Control Conference; Vol. 2006).

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

TY - GEN

T1 - Spatial controllability and multiple actuator placement for dissipative partial differential equation systems

AU - Armaou, Antonios

AU - Demetriou, Michael A.

PY - 2006/12/1

Y1 - 2006/12/1

N2 - This manuscript considers the problem of actuator placement for transport-reaction processes, which are mathematically modelled by linear parabolic partial differential equations. The novelty of the proposed optimization scheme is that it considers the controllability of specific modes while at the same time minimizes the spillover effects due to intermediate range modes. Using modal decomposition for space discretization, along with the notions of spatial and modal controllabilities, the semi-infinite optimization problem is formulated as a nonlinear optimization problem in appropriate L? spaces. To address the problem of actuator clusterization, a modification to earlier efforts is introduced, which takes the form of an additional constraint in the location optimization. The formulated optimization problem is subsequently solved using standard search algorithms. The proposed method is successfully applied to a representative process, modelled by a one-dimensional parabolic PDE, where the optimal location of multiple actuators is computed.

AB - This manuscript considers the problem of actuator placement for transport-reaction processes, which are mathematically modelled by linear parabolic partial differential equations. The novelty of the proposed optimization scheme is that it considers the controllability of specific modes while at the same time minimizes the spillover effects due to intermediate range modes. Using modal decomposition for space discretization, along with the notions of spatial and modal controllabilities, the semi-infinite optimization problem is formulated as a nonlinear optimization problem in appropriate L? spaces. To address the problem of actuator clusterization, a modification to earlier efforts is introduced, which takes the form of an additional constraint in the location optimization. The formulated optimization problem is subsequently solved using standard search algorithms. The proposed method is successfully applied to a representative process, modelled by a one-dimensional parabolic PDE, where the optimal location of multiple actuators is computed.

UR - http://www.scopus.com/inward/record.url?scp=34047223488&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34047223488&partnerID=8YFLogxK

M3 - Conference contribution

SN - 1424402107

SN - 9781424402106

T3 - Proceedings of the American Control Conference

SP - 1473

EP - 1480

BT - Proceedings of the 2006 American Control Conference

ER -

Armaou A, Demetriou MA. Spatial controllability and multiple actuator placement for dissipative partial differential equation systems. In Proceedings of the 2006 American Control Conference. 2006. p. 1473-1480. 1656426. (Proceedings of the American Control Conference).

Access to Document