WIAS Preprint No. 2287, (2016)

Optimal sensor placement: A robust approach


Authors

  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Rautenberg, Carlos N.
    ORCID: 0000-0001-9497-9296
  • Mohammadi, Masoumeh
  • Kanitsar, Martin

2010 Mathematics Subject Classification

  • 35K86 47J20 49J40 49M15 65J15 65K10

Keywords

  • Sensor placement, trace class operators, sensitivities, Riccati equation

DOI

10.20347/WIAS.PREPRINT.2287

Abstract

We address the problem of optimally placing sensor networks for convection-diffusion processes where the convective part is perturbed. The problem is formulated as an optimal control problem where the integral Riccati equation is a constraint and the design variables are sensor locations. The objective functional involves a term associated to the trace of the solution to the Riccati equation and a term given by a constrained optimization problem for the directional derivative of the previous quantity over a set of admissible perturbations. The paper addresses the existence of the derivative with respect to the convective part of the solution to the Riccati equation, the well-posedness of the optimization problem and finalizes with a range of numerical tests.

Appeared in

  • SIAM J. Control Optim., 55 (2017), pp. 3609--3639.

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