Economic model predictive control of parabolic PDE systems: Handling state constraints by adaptive proper orthogonal decomposition

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

Research output: Contribution to journalConference article

Abstract

Economic model predictive control (EMPC) is becoming increasingly popular within the control community owing to its combination of feedback control and dynamic economic optimization of the system/process dynamics. In this paper, we consider systems described by parabolic partial differential equations (PDEs), and apply Galerkin's method with adaptive proper orthogonal decomposition methodology (APOD) to construct reduced-order models on-line of varying accuracy which are used by an EMPC system to compute control actions for the PDE system. APOD is superior than using proper orthogonal decomposition methodology (POD) with off-line computed empirical eigenfunctions owing to the fact that the reduced-order model is updated on-line. A new EMPC scheme is proposed which can successfully improve the computational efficiency of EMPC while avoiding state constraint violation by integrating the APOD method with a high-order finite-difference method. The computational approaches presented are demonstrated using a tubular reactor example.

Original languageEnglish (US)
Article number7039812
Pages (from-to)2758-2763
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume2015-February
Issue numberFebruary
DOIs
StatePublished - Jan 1 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

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Orthogonal Decomposition
Economic Model
State Constraints
Parabolic Partial Differential Equations
Model predictive control
Model Predictive Control
Partial differential equations
Decomposition
Economics
Reduced Order Model
Methodology
Predictive control systems
Dynamic Process
Galerkin Method
Computational Efficiency
Feedback Control
Reactor
Difference Method
Eigenfunctions
Galerkin methods

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

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abstract = "Economic model predictive control (EMPC) is becoming increasingly popular within the control community owing to its combination of feedback control and dynamic economic optimization of the system/process dynamics. In this paper, we consider systems described by parabolic partial differential equations (PDEs), and apply Galerkin's method with adaptive proper orthogonal decomposition methodology (APOD) to construct reduced-order models on-line of varying accuracy which are used by an EMPC system to compute control actions for the PDE system. APOD is superior than using proper orthogonal decomposition methodology (POD) with off-line computed empirical eigenfunctions owing to the fact that the reduced-order model is updated on-line. A new EMPC scheme is proposed which can successfully improve the computational efficiency of EMPC while avoiding state constraint violation by integrating the APOD method with a high-order finite-difference method. The computational approaches presented are demonstrated using a tubular reactor example.",
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Economic model predictive control of parabolic PDE systems : Handling state constraints by adaptive proper orthogonal decomposition. / Lao, Liangfeng; Ellis, Matthew; Armaou, Antonios; Christofides, Panagiotis D.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2015-February, No. February, 7039812, 01.01.2014, p. 2758-2763.

Research output: Contribution to journalConference article

TY - JOUR

T1 - Economic model predictive control of parabolic PDE systems

T2 - Handling state constraints by adaptive proper orthogonal decomposition

AU - Lao, Liangfeng

AU - Ellis, Matthew

AU - Armaou, Antonios

AU - Christofides, Panagiotis D.

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