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A New Lagrange-Newton-Krylov Solver for PDE-constrained Nonlinear Model Predictive Control
- Source :
- Christiansen , L H & Jørgensen , J B 2018 , ' A New Lagrange-Newton-Krylov Solver for PDE-constrained Nonlinear Model Predictive Control ' , I F A C Workshop Series , vol. 51 , no. 20 , pp. 325-330 .
- Publication Year :
- 2018
-
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.
Details
- Database :
- OAIster
- Journal :
- Christiansen , L H & Jørgensen , J B 2018 , ' A New Lagrange-Newton-Krylov Solver for PDE-constrained Nonlinear Model Predictive Control ' , I F A C Workshop Series , vol. 51 , no. 20 , pp. 325-330 .
- Notes :
- application/pdf, English
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1083513698
- Document Type :
- Electronic Resource