A fast PDE-constrained optimization solver for nonlinear diffusion-reaction processes

Lasse Hjuler Christiansen, John Bagterp Jørgensen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Large-scale nonlinear model predictive control (NMPC) often relies on real-time solution of optimization problems that are constrained by partial differential equations (PDEs). However, the size and complexity of the underlying PDEs present significant computational challenges. In this regard, the development of fast, efficient and scalable PDEconstrained optimization solvers remains central to large-scale NMPC. As a contribution in this direction, this paper proposes a new efficient preconditioned iterative scheme for optimal control of large-scale time-dependent diffusion-reaction problems with nonlinear reaction kinetics. The scheme combines a custom-made high-order spectral Petrov-Galerkin (SPG) method with a new preconditioner tailored for the linearquadratic control problems that underly Sequential Quadratic Programming (SQP) methods. The preconditioner is matrixfree and amenable to parallelization. To demonstrate efficiency, a case study applies the SPG scheme to control solid fuel ignition (SFI) processes. In the absence of control, such processes lead to unstable systems that naturally exhibit finite-time blow-up phenomena. Open-loop simulations demonstrate the ability of the SPG scheme to efficiently control SFI processes, independently of the problem size and the model parameters.
Original languageEnglish
Title of host publication2018 IEEE Conference on Decision and Control
PublisherIEEE
Publication date2018
Pages2635-2640
ISBN (Electronic)978-1-5386-1395-5
DOIs
Publication statusPublished - 2018
Event57th IEEE Conference on Decision and Control - Fontainebleau , Miami, United States
Duration: 17 Dec 201819 Dec 2018
https://cdc2018.ieeecss.org/

Conference

Conference57th IEEE Conference on Decision and Control
LocationFontainebleau
CountryUnited States
CityMiami
Period17/12/201819/12/2018
Internet address

Cite this

Christiansen, L. H., & Jørgensen, J. B. (2018). A fast PDE-constrained optimization solver for nonlinear diffusion-reaction processes. In 2018 IEEE Conference on Decision and Control (pp. 2635-2640). IEEE. https://doi.org/10.1109/CDC.2018.8619280
Christiansen, Lasse Hjuler ; Jørgensen, John Bagterp. / A fast PDE-constrained optimization solver for nonlinear diffusion-reaction processes. 2018 IEEE Conference on Decision and Control. IEEE, 2018. pp. 2635-2640
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title = "A fast PDE-constrained optimization solver for nonlinear diffusion-reaction processes",
abstract = "Large-scale nonlinear model predictive control (NMPC) often relies on real-time solution of optimization problems that are constrained by partial differential equations (PDEs). However, the size and complexity of the underlying PDEs present significant computational challenges. In this regard, the development of fast, efficient and scalable PDEconstrained optimization solvers remains central to large-scale NMPC. As a contribution in this direction, this paper proposes a new efficient preconditioned iterative scheme for optimal control of large-scale time-dependent diffusion-reaction problems with nonlinear reaction kinetics. The scheme combines a custom-made high-order spectral Petrov-Galerkin (SPG) method with a new preconditioner tailored for the linearquadratic control problems that underly Sequential Quadratic Programming (SQP) methods. The preconditioner is matrixfree and amenable to parallelization. To demonstrate efficiency, a case study applies the SPG scheme to control solid fuel ignition (SFI) processes. In the absence of control, such processes lead to unstable systems that naturally exhibit finite-time blow-up phenomena. Open-loop simulations demonstrate the ability of the SPG scheme to efficiently control SFI processes, independently of the problem size and the model parameters.",
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Christiansen, LH & Jørgensen, JB 2018, A fast PDE-constrained optimization solver for nonlinear diffusion-reaction processes. in 2018 IEEE Conference on Decision and Control. IEEE, pp. 2635-2640, 57th IEEE Conference on Decision and Control, Miami, United States, 17/12/2018. https://doi.org/10.1109/CDC.2018.8619280

A fast PDE-constrained optimization solver for nonlinear diffusion-reaction processes. / Christiansen, Lasse Hjuler; Jørgensen, John Bagterp.

2018 IEEE Conference on Decision and Control. IEEE, 2018. p. 2635-2640.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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N2 - Large-scale nonlinear model predictive control (NMPC) often relies on real-time solution of optimization problems that are constrained by partial differential equations (PDEs). However, the size and complexity of the underlying PDEs present significant computational challenges. In this regard, the development of fast, efficient and scalable PDEconstrained optimization solvers remains central to large-scale NMPC. As a contribution in this direction, this paper proposes a new efficient preconditioned iterative scheme for optimal control of large-scale time-dependent diffusion-reaction problems with nonlinear reaction kinetics. The scheme combines a custom-made high-order spectral Petrov-Galerkin (SPG) method with a new preconditioner tailored for the linearquadratic control problems that underly Sequential Quadratic Programming (SQP) methods. The preconditioner is matrixfree and amenable to parallelization. To demonstrate efficiency, a case study applies the SPG scheme to control solid fuel ignition (SFI) processes. In the absence of control, such processes lead to unstable systems that naturally exhibit finite-time blow-up phenomena. Open-loop simulations demonstrate the ability of the SPG scheme to efficiently control SFI processes, independently of the problem size and the model parameters.

AB - Large-scale nonlinear model predictive control (NMPC) often relies on real-time solution of optimization problems that are constrained by partial differential equations (PDEs). However, the size and complexity of the underlying PDEs present significant computational challenges. In this regard, the development of fast, efficient and scalable PDEconstrained optimization solvers remains central to large-scale NMPC. As a contribution in this direction, this paper proposes a new efficient preconditioned iterative scheme for optimal control of large-scale time-dependent diffusion-reaction problems with nonlinear reaction kinetics. The scheme combines a custom-made high-order spectral Petrov-Galerkin (SPG) method with a new preconditioner tailored for the linearquadratic control problems that underly Sequential Quadratic Programming (SQP) methods. The preconditioner is matrixfree and amenable to parallelization. To demonstrate efficiency, a case study applies the SPG scheme to control solid fuel ignition (SFI) processes. In the absence of control, such processes lead to unstable systems that naturally exhibit finite-time blow-up phenomena. Open-loop simulations demonstrate the ability of the SPG scheme to efficiently control SFI processes, independently of the problem size and the model parameters.

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