文章基本信息

标题：A New Lagrange-Newton-Krylov Solver for PDE-constrained Nonlinear Model Predictive Control
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作者：Lasse Hjuler Christiansen ; John Bagterp Jørgensen
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2018
卷号：51
期号：20
页码：325-330
DOI：10.1016/j.ifacol.2018.11.053
语种：English
出版社：Elsevier
摘要：AbstractReal-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 106unknowns can be solved efficiently in less than a minute.
关键词：KeywordsOptimal controlModel-based controlNonlinear controlPartial differential equationsLarge-scale systemsIterative methods