A New Lagrange-Newton-Krylov Solver for PDE-constrained Nonlinear Model Predictive Control
Research output: Research - peer-review › Conference article – Annual report year: 2018
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 language | English |
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Journal | IFAC-PapersOnLine |
Volume | 51 |
Issue number | 20 |
Pages (from-to) | 325-330 |
ISSN | 2405-8963 |
DOIs | |
State | Published - 2018 |
Event | 6th IFAC Conference on Nonlinear Model Predictive Control (NMPC 2018) - Madison, United States Duration: 19 Aug 2018 → 22 Aug 2018 |
Conference
Conference | 6th IFAC Conference on Nonlinear Model Predictive Control (NMPC 2018) |
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Country | United States |
City | Madison |
Period | 19/08/2018 → 22/08/2018 |
Citations | Web of Science® Times Cited: 0 |
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- Optimal control, Model-based control, Nonlinear control, Partial differential equations, Large-scale systems, Iterative methods
Research areas
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