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Solving ODE for Optimization

In: Optimization and Inverse Problems in Electromagnetism

Author

Listed:
  • Vincent Fischer

    (ENSIEG, Laboratoire d’Electrotechnique de Grenoble (INPG / UJF — CNRS . UMR 5529))

  • Laurent Gerbaud

    (ENSIEG, Laboratoire d’Electrotechnique de Grenoble (INPG / UJF — CNRS . UMR 5529))

Abstract

The paper deals with the sizing of some electrical devices, mainly electrical circuits, using optimization under constraints. More accurately, gradient optimization algorithms are considered. So, the derivatives of the outputs of the sizing model according to its inputs have to be valued. In electrical devices, some sizing criteria may require the solving of ordinary differential equation (ODE). E.g, this may concerns maximum values, r.m.s. values, values of some variables at a specific date, etc. Several methods may be used to solve such ODE : symbolic, numerical or a mix of them. In the specific case of systems modelled by linear state equations — e.g. electrical circuits- an approach based on matrix exponential is proposed to solve corresponding ODEs. After a presentation of the interests of the proposed approach compared to simulation in the field of gradient optimization, the paper presents the ODE solving and the chosen matrix exponential methods. Finally, the method is applied on some electrical circuits.

Suggested Citation

  • Vincent Fischer & Laurent Gerbaud, 2003. "Solving ODE for Optimization," Springer Books, in: Marek Rudnicki & Sławomir Wiak (ed.), Optimization and Inverse Problems in Electromagnetism, pages 71-78, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2494-4_8
    DOI: 10.1007/978-94-017-2494-4_8
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