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@ARTICLE{Schultz:917577,
      author       = {Schultz, Eduardo S. and Olofsson, Simon and Mhamdi, Adel
                      and Mitsos, Alexander},
      title        = {{S}atisfaction of path chance constraints in dynamic
                      optimization problems},
      journal      = {Computers $\&$ chemical engineering},
      volume       = {164},
      issn         = {0098-1354},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier Science},
      reportid     = {FZJ-2023-00779},
      pages        = {107899 -},
      year         = {2022},
      abstract     = {We propose an algorithm that calculates heuristically
                      optimal solutions for dynamic optimization problems with
                      path chance constraints. The solution is a feasible point in
                      the chance constraint sense and an optimal point of an
                      approximated problem. Uncertainty in parameters and initial
                      conditions is modelled as Gaussian distributions. The method
                      solves nonlinear programs (NLP) generated by replacing the
                      probability constraint by a set of approximated
                      deterministic pointwise constraints with a right-hand side
                      restriction. For each NLP solution, the probability of
                      constraint violation is calculated by Monte Carlo
                      integration. When the NLP solution does not respect the
                      chance constraint, new pointwise constraints are added, and
                      we update the approximation and the restriction with the
                      results from Monte Carlo integration. These steps are
                      repeated until a feasible solution is found. The algorithm
                      terminates after a finite number of iterations under mild
                      assumptions. We demonstrate the algorithm in a fed-batch
                      bioreactor case study, showing that it provides a solution
                      in a shorter CPU time and fewer iterations when compared to
                      using a fixed set of pointwise constraints where only the
                      restriction is updated.},
      cin          = {IEK-10},
      ddc          = {660},
      cid          = {I:(DE-Juel1)IEK-10-20170217},
      pnm          = {899 - ohne Topic (POF4-899)},
      pid          = {G:(DE-HGF)POF4-899},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000926599000004},
      doi          = {10.1016/j.compchemeng.2022.107899},
      url          = {https://juser.fz-juelich.de/record/917577},
}