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

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Abstract

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.

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  1. Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, TX, 78712, USA

    Georg Stadler

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  1. Georg Stadler
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Correspondence to Georg Stadler.

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Stadler, G. Elliptic optimal control problems with L 1-control cost and applications for the placement of control devices. Comput Optim Appl 44, 159–181 (2009). https://doi.org/10.1007/s10589-007-9150-9

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  • DOI: https://doi.org/10.1007/s10589-007-9150-9

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