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Elliptic optimal control problems with L (1)-control cost and applications for the placement of control devices

Computational optimization and applications, 2009-11, Vol.44 (2), p.159-181 [Peer Reviewed Journal]

ISSN: 0926-6003 ;EISSN: 1573-2894 ;DOI: 10.1007/s10589-007-9150-9

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  • Title:
    Elliptic optimal control problems with L (1)-control cost and applications for the placement of control devices
  • Author: Stadler, Georg
  • Is Part Of: Computational optimization and applications, 2009-11, Vol.44 (2), p.159-181
  • Description: Elliptic optimal control problems with L (1)-control cost are analyzed. Due to the nonsmooth objective functional the optimal controls are identically zero on large parts of the control domain. For applications, in which one cannot put control devices (or actuators) all over the control domain, this provides information about where it is most efficient to put them. We analyze structural properties of L (1)-control cost solutions. For solving the non-differentiable optimal control problem we propose a semismooth Newton method that can be stated and analyzed in function space and converges locally with a superlinear rate. Numerical tests on model problems show the usefulness of the approach for the location of control devices and the efficiency of our algorithm.
  • Language: English
  • Identifier: ISSN: 0926-6003
    EISSN: 1573-2894
    DOI: 10.1007/s10589-007-9150-9
  • Source: Alma/SFX Local Collection
    ProQuest Central
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