A control-oriented approach to optimal sensor placement

TL;DR

This paper introduces a control-oriented optimal experimental design framework for linear PDE-constrained Bayesian inverse problems, focusing on sensor placement that minimizes uncertainty in the controlled state or objective.

Contribution

It develops a novel mathematical framework and scalable computational methods for sensor placement tailored to control-oriented inverse problems with PDE constraints.

Findings

Proposes a control-oriented sensor placement methodology.

Provides scalable algorithms for uncertainty quantification.

Demonstrates effectiveness through heat transfer application examples.

Abstract

We propose a control-oriented optimal experimental design (cOED) approach for linear PDE-constrained Bayesian inverse problems. In particular, we consider optimal control problems with uncertain parameters that need to be estimated by solving an inverse problem, which in turn requires measurement data. We consider the case where data is collected at a set of sensors. While classical Bayesian OED techniques provide experimental designs (sensor placements) that minimize the posterior uncertainty in the inversion parameter, these designs are not tailored to the demands of the optimal control problem. In the present control-oriented setting, we prioritize the designs that minimize the uncertainty in the state variable being controlled or the control objective. We propose a mathematical framework for uncertainty quantification and cOED for parameterized PDE-constrained optimal control problems with linear dependence to the control variable and the inversion parameter. We also present scalable computational methods for computing control-oriented sensor placements and for quantifying the uncertainty in the control objective. Additionally, we present illustrative numerical results in the context of a model problem motivated by heat transfer applications.