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

Lasse Hjuler Christiansen*, John Bagterp Jørgensen

*Corresponding author for this work

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Abstract

Real-time optimization of systems governed by partial differential equations (PDEs) presents significant computational challenges to nonlinear model predictive control (NMPC). The large-scale nature of PDEs often limits the use of standard nested black-box optimizers that require repeated forward simulations and expensive gradient computations. Hence, to ensure online solutions at relevant time-scales, large-scale NMPC algorithms typically require powerful, customized PDE-constrained optimization solvers. To this end, this paper proposes a new Lagrange-Newton-Krylov (LNK) method that targets the class of time-dependent nonlinear diffusion-reaction systems arising from chemical processes. The LNK solver combines a high-order spectral Petrov-Galerkin (SPG) method with a new, parallel preconditioner tailored for the large-scale saddle-point systems that form subproblems of Sequential Quadratic Programming (SQP) methods. To establish proof-of-concept, a case study uses a simple parallel MATLAB implementation of the preconditioner with 10 cores. As a step towards real-time control, the results demonstrate that large-scale diffusion-reaction optimization problems with more than 106 unknowns can be solved efficiently in less than a minute.
Original languageEnglish
Book seriesI F A C Workshop Series
Volume51
Issue number20
Pages (from-to)325-330
ISSN1474-6670
DOIs
Publication statusPublished - 2018
Event6th IFAC Conference on Nonlinear Model Predictive Control (NMPC 2018) - Madison, United States
Duration: 19 Aug 201822 Aug 2018

Conference

Conference6th IFAC Conference on Nonlinear Model Predictive Control (NMPC 2018)
CountryUnited States
CityMadison
Period19/08/201822/08/2018

Keywords

  • Optimal control
  • Model-based control
  • Nonlinear control
  • Partial differential equations
  • Large-scale systems
  • Iterative methods

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