In this talk, we consider optimal experimental design (OED) for
infinite-dimensional Bayesian inverse problems, with a focus on optimal sensor
placement. Traditional OED approaches seek sensor placements that minimize
uncertainty in the estimated model parameters. However, in some cases, parameter
estimation is an intermediate step towards a downstream goal of solving an
optimal control problem.  In this setting, a sensor placement that is optimal for parameter estimation may be suboptimal for the demands of the optimal control problem.  To address this, we propose a control-oriented OED (cOED) framework.  Namely, we seek sensor placements that minimize uncertainty in the state being controlled or in the control objective.  In the talk, I will discuss our proposed mathematical and computational framework for cOED for infinite-dimensional Bayesian linear inverse problems governed by PDEs. The focus is on optimal control problems with linear dependence on the control variable and the inversion parameter.  We will also consider some numerical results in the context of a model problem motivated by heat transfer problems.