Optimal sensor placement: A robust approach
- Hintermüller, Michael
- Rautenberg, Carlos N.
- Mohammadi, Masoumeh
- Kanitsar, Martin
2010 Mathematics Subject Classification
- 35K86 47J20 49J40 49M15 65J15 65K10
- Sensor placement, trace class operators, sensitivities, Riccati equation
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.
- SIAM J. Control Optim., 55 (2017), pp. 3609--3639.