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@INPROCEEDINGS{Warnecke:645013,
      author       = {Warnecke, Torben and Lichtenberg, Gerwald},
      title        = {{A}pproach for the {M}ode {S}witching {P}roblem in
                      {P}iecewise {S}mooth {I}mplicit {M}ultilinear {IVP}s},
      publisher    = {SCITEPRESS - Science and Technology Publications},
      reportid     = {PUBDB-2026-00536},
      pages        = {349-356},
      year         = {2025},
      comment      = {Proceedings of the 15th International Conference on
                      Simulation and Modeling Methodologies, Technologies and
                      Applications - SCITEPRESS - Science and Technology
                      Publications, 2025. - ISBN 978-989-758-759-7 -
                      doi:10.5220/0013578200003970},
      booktitle     = {Proceedings of the 15th International
                       Conference on Simulation and Modeling
                       Methodologies, Technologies and
                       Applications - SCITEPRESS - Science and
                       Technology Publications, 2025. - ISBN
                       978-989-758-759-7 -
                       doi:10.5220/0013578200003970},
      abstract     = {This paper addresses the mode switching problem in
                      piecewise smooth implicit multilinear initial value problems
                      (IVPs), which are relevant for modeling hybrid dynamical
                      systems like HVAC and power systems. Unlike traditional
                      switched systems with explicit mode descriptions, this work
                      focuses on systems where mode information is implicitly
                      encoded in binary-valued variables and switching conditions
                      are defined by inequality constraints. The paper
                      investigates the transversal motion discontinuities that
                      occur when the system meets the boundary surfaces defined by
                      these constraints. A method is presented to determine the
                      discontinuous motion by analyzing the total derivative of
                      the inequality constraints. The modeling framework utilizes
                      hybrid implicit multilinear time-invariant (iMTI) functions
                      and describes the system using inequality-constrained
                      index-1 differential-algebraic equations (DAEs). The
                      Jacobian matrices and thus the total derivatives can be
                      estimated algebraically, due to the use of multilinear
                      functions. To handle the combinatorial complexity associated
                      with the binary variables during mode switching, the paper
                      proposes using sparsity pattern analysis to identify and
                      solve sub-problems more efficiently. The presented method is
                      applied to a two-point temperature-controlled three-tank
                      system, and simulations are performed using the MTI-Toolbox
                      for MathWorks MATLAB.},
      month         = {Jun},
      date          = {2025-06-11},
      organization  = {15th International Conference on
                       Simulation and Modeling Methodologies,
                       Technologies and Applications, Bilbao
                       (Spain), 11 Jun 2025 - 13 Jun 2025},
      cin          = {MKK3},
      cid          = {I:(DE-H253)MKK3-20210408},
      pnm          = {621 - Accelerator Research and Development (POF4-621)},
      pid          = {G:(DE-HGF)POF4-621},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)8 / PUB:(DE-HGF)7},
      doi          = {10.5220/0013578200003970},
      url          = {https://bib-pubdb1.desy.de/record/645013},
}