Conference paper
A New Lagrange-Newton-Krylov Solver for PDE-constrained Nonlinear Model Predictive Control
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.
Language: | English |
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Year: | 2018 |
Pages: | 325-330 |
Proceedings: | 6th IFAC Conference on Nonlinear Model Predictive Control (NMPC 2018) |
ISSN: | 14746670 |
Types: | Conference paper |
DOI: | 10.1016/j.ifacol.2018.11.053 |
ORCIDs: | Christiansen, Lasse Hjuler and Jørgensen, John Bagterp |