A New Lagrange-Newton-Krylov Solver for PDE-constrained Nonlinear Model Predictive Control

Christiansen, Lasse Hjuler; Jørgensen, John Bagterp

doi:10.1016/j.ifacol.2018.11.053

Cited by 3 publications

(4 citation statements)

References 19 publications

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“…This paper contributes to a recent series of efforts by the authors that seek to construct fast, iterative solvers for a range of PDE-constrained optimization problems by exploiting the properties of customized spectral bases [4][5][6]. This series of work aims to introduce a high-order alternative to the widely-used constellation of low-order finite-element methods and Schur-complement preconditioners that currently predominates the literature on PDE control [12][13][14].…”

Section: Main Contributions and Outlinementioning

confidence: 99%

New Preconditioners for Semi-linear PDE-Constrained Optimal Control in Annular Geometries

Christiansen

Jørgensen

2020

Lecture Notes in Computational Science and Engineering

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Optimization problems that are constrained by partial differential equations (PDEs) often pose significant computational challenges to black-box optimization algorithms. This is particular the case for non-linear problems that typically rely on multi-query solution of large-scale linearized subsystems. In this regard, this paper proposes a customized solution strategy for a class of semi-linear PDE-constrained optimization problems in annular domains. At its core, the strategy relies on a collection of new Poisson-like preconditioners that are based on boundary-adapted spectral Galerkin methods. The preconditioners are matrix-free and scale linearly with the problem size. To establish proof-of-concept, a case study solves a benchmark control problem for various model parameters. The results show that the preconditioners lead to fast solution strategies that outperform conventional direct approaches.

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Section: Main Contributions and Outlinementioning

confidence: 99%

New Preconditioners for Semi-linear PDE-Constrained Optimal Control in Annular Geometries

Christiansen

Jørgensen

2020

Lecture Notes in Computational Science and Engineering

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“…and with initial and boundary conditions as given in (4). While (5) are linear, the problem of opposite time evolutions of the state and the adjoint state remains.…”

Section: B Optimality Systemmentioning

confidence: 99%

“…The initial value problem (IVP), (1), is a general form of advection-reaction-diffusion equations with linear diffusion. Processes of this type encapsulates a great amount of physical phenomena, such as chemical reactions [4], fluid flows [14], and predator-prey systems [15].…”

Section: Optimal Control Of Nonlinear Pdesmentioning

confidence: 99%

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Reduced Order Modeling for Nonlinear PDE-constrained Optimization using Neural Networks

Mücke

Christiansen

Engsig-Karup

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential equations (PDEs), black-box optimizers are rarely sufficient to get the required online computational speed. In such cases one must resort to customized solvers. This paper present a new solver for nonlinear time-dependent PDE-constrained optimization problems. It is composed of a sequential quadratic programming (SQP) scheme to solve the PDE-constrained problem in an offline phase, a proper orthogonal decomposition (POD) approach to identify a lower dimensional solution space, and a neural network (NN) for fast online evaluations. The proposed method is showcased on a regularized least-square optimal control problem for the viscous Burgers' equation. It is concluded that significant online speed-up is achieved, compared to conventional methods using SQP and finite elements, at a cost of a prolonged offline phase and reduced accuracy.

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

Christiansen

Jørgensen

2018

2018 IEEE Conference on Decision and Control (CDC)

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A New Lagrange-Newton-Krylov Solver for PDE-constrained Nonlinear Model Predictive Control

Cited by 3 publications

References 19 publications

New Preconditioners for Semi-linear PDE-Constrained Optimal Control in Annular Geometries

New Preconditioners for Semi-linear PDE-Constrained Optimal Control in Annular Geometries

Reduced Order Modeling for Nonlinear PDE-constrained Optimization using Neural Networks

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

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