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@INPROCEEDINGS{Doncevic:894319,
      author       = {Doncevic, Danimir and Schweidtmann, Artur M. and Vaupel,
                      Yannic and Schäfer, Pascal and Caspari, Adrian and Mitsos,
                      Alexander},
      title        = {{D}eterministic {G}lobal {N}onlinear {M}odel {P}redictive
                      {C}ontrol with {N}eural {N}etworks {E}mbedded},
      journal      = {IFAC-PapersOnLine},
      volume       = {53},
      number       = {2},
      issn         = {2405-8963},
      address      = {Laxenburg},
      publisher    = {IFAC},
      reportid     = {FZJ-2021-03179},
      pages        = {5273 - 5278},
      year         = {2020},
      abstract     = {Nonlinear model predictive control requires the solution of
                      nonlinear programs with potentially multiple local
                      solutions. Here, deterministic global optimization can
                      guarantee to find a global optimum. However, its application
                      is currently severely limited by computational cost and
                      requires further developments in problem formulation,
                      optimization solvers, and computing architectures. In this
                      work, we propose a reduced-space formulation for the global
                      optimization of problems with recurrent neural networks
                      (RNN) embedded, based on our recent work on feed-forward
                      artificial neural networks embedded. The method reduces the
                      dimensionality of the optimization problem significantly,
                      lowering the computational cost. We implement the NMPC
                      problem in our open-source solver MAiNGO and solve it using
                      parallel computing on 40 cores. We demonstrate real-time
                      capability for the illustrative van de Vusse CSTR case
                      study. We further propose two alternatives to reduce
                      computational time: i) reformulate the RNN model by exposing
                      a selected state variable to the optimizer; ii) replace the
                      RNN with a neural multi-model. In our numerical case studies
                      each proposal results in a reduction of computational time
                      by an order of magnitude.},
      month         = {Jul},
      date          = {2020-07-11},
      organization  = {1st Virtual IFAC World Congress,
                       online (Germany), 11 Jul 2020 - 17 Jul
                       2020},
      cin          = {IEK-10},
      ddc          = {600},
      cid          = {I:(DE-Juel1)IEK-10-20170217},
      pnm          = {1121 - Digitalization and Systems Technology for
                      Flexibility Solutions (POF4-112)},
      pid          = {G:(DE-HGF)POF4-1121},
      typ          = {PUB:(DE-HGF)16 / PUB:(DE-HGF)8},
      UT           = {WOS:000652593000151},
      doi          = {10.1016/j.ifacol.2020.12.1207},
      url          = {https://juser.fz-juelich.de/record/894319},
}