Economic model predictive control of parabolic PDE systems using empirical eigenfunctions

Liangfeng Lao; Matthew Ellis; Antonios Armaou; Panagiotis D. Christofides

doi:10.1109/ACC.2014.6858761

Economic model predictive control of parabolic PDE systems using empirical eigenfunctions

Liangfeng Lao, Matthew Ellis, Antonios Armaou, Panagiotis D. Christofides

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

Abstract

This work focuses on the development of reduced-order models (ROMs) of transport-reaction processes described by nonlinear parabolic partial differential equations (PDEs) and their application in the formulation of economic model predictive control (EMPC) systems. Specifically, the reduced-order models of the PDEs are constructed on the basis of historical data-based empirical eigenfunctions by applying Karhunen-Loève expansion. Several EMPC systems each using a different ROM (i.e., different number of modes and derived from either using analytical sinusoidal/cosinusoidal eigenfunctions or empirical eigenfunctions as basis functions) are applied to a tubular reactor example where a second-order reaction occurs. The model accuracy, computational time and closed-loop economic performance of the closed-loop tubular reactor under the different EMPC systems are compared.

Original language	English (US)
Title of host publication	2014 American Control Conference, ACC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3375-3380
Number of pages	6
ISBN (Print)	9781479932726
DOIs	https://doi.org/10.1109/ACC.2014.6858761
State	Published - 2014
Event	2014 American Control Conference, ACC 2014 - Portland, OR, United States Duration: Jun 4 2014 → Jun 6 2014

Publication series

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

Other

Other	2014 American Control Conference, ACC 2014
Country/Territory	United States
City	Portland, OR
Period	6/4/14 → 6/6/14

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

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10.1109/ACC.2014.6858761

Cite this

Lao, L., Ellis, M., Armaou, A., & Christofides, P. D. (2014). Economic model predictive control of parabolic PDE systems using empirical eigenfunctions. In 2014 American Control Conference, ACC 2014 (pp. 3375-3380). Article 6858761 (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2014.6858761

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title = "Economic model predictive control of parabolic PDE systems using empirical eigenfunctions",

abstract = "This work focuses on the development of reduced-order models (ROMs) of transport-reaction processes described by nonlinear parabolic partial differential equations (PDEs) and their application in the formulation of economic model predictive control (EMPC) systems. Specifically, the reduced-order models of the PDEs are constructed on the basis of historical data-based empirical eigenfunctions by applying Karhunen-Lo{\`e}ve expansion. Several EMPC systems each using a different ROM (i.e., different number of modes and derived from either using analytical sinusoidal/cosinusoidal eigenfunctions or empirical eigenfunctions as basis functions) are applied to a tubular reactor example where a second-order reaction occurs. The model accuracy, computational time and closed-loop economic performance of the closed-loop tubular reactor under the different EMPC systems are compared.",

author = "Liangfeng Lao and Matthew Ellis and Antonios Armaou and Christofides, {Panagiotis D.}",

year = "2014",

doi = "10.1109/ACC.2014.6858761",

language = "English (US)",

isbn = "9781479932726",

series = "Proceedings of the American Control Conference",

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

pages = "3375--3380",

booktitle = "2014 American Control Conference, ACC 2014",

address = "United States",

note = "2014 American Control Conference, ACC 2014 ; Conference date: 04-06-2014 Through 06-06-2014",

}

Lao, L, Ellis, M, Armaou, A & Christofides, PD 2014, Economic model predictive control of parabolic PDE systems using empirical eigenfunctions. in 2014 American Control Conference, ACC 2014., 6858761, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 3375-3380, 2014 American Control Conference, ACC 2014, Portland, OR, United States, 6/4/14. https://doi.org/10.1109/ACC.2014.6858761

Economic model predictive control of parabolic PDE systems using empirical eigenfunctions. / Lao, Liangfeng; Ellis, Matthew; Armaou, Antonios et al.
2014 American Control Conference, ACC 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 3375-3380 6858761 (Proceedings of the American Control Conference).

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

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T1 - Economic model predictive control of parabolic PDE systems using empirical eigenfunctions

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AU - Ellis, Matthew

AU - Armaou, Antonios

AU - Christofides, Panagiotis D.

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N2 - This work focuses on the development of reduced-order models (ROMs) of transport-reaction processes described by nonlinear parabolic partial differential equations (PDEs) and their application in the formulation of economic model predictive control (EMPC) systems. Specifically, the reduced-order models of the PDEs are constructed on the basis of historical data-based empirical eigenfunctions by applying Karhunen-Loève expansion. Several EMPC systems each using a different ROM (i.e., different number of modes and derived from either using analytical sinusoidal/cosinusoidal eigenfunctions or empirical eigenfunctions as basis functions) are applied to a tubular reactor example where a second-order reaction occurs. The model accuracy, computational time and closed-loop economic performance of the closed-loop tubular reactor under the different EMPC systems are compared.

AB - This work focuses on the development of reduced-order models (ROMs) of transport-reaction processes described by nonlinear parabolic partial differential equations (PDEs) and their application in the formulation of economic model predictive control (EMPC) systems. Specifically, the reduced-order models of the PDEs are constructed on the basis of historical data-based empirical eigenfunctions by applying Karhunen-Loève expansion. Several EMPC systems each using a different ROM (i.e., different number of modes and derived from either using analytical sinusoidal/cosinusoidal eigenfunctions or empirical eigenfunctions as basis functions) are applied to a tubular reactor example where a second-order reaction occurs. The model accuracy, computational time and closed-loop economic performance of the closed-loop tubular reactor under the different EMPC systems are compared.

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Economic model predictive control of parabolic PDE systems using empirical eigenfunctions

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