A control-oriented approach to optimal sensor placement
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909758969085952 |
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| author | Madhavan, Madhusudan Alexanderian, Alen Saibaba, Arvind K. Waanders, Bart van Bloemen White, Rebekah D. |
| author_facet | Madhavan, Madhusudan Alexanderian, Alen Saibaba, Arvind K. Waanders, Bart van Bloemen White, Rebekah D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15062 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A control-oriented approach to optimal sensor placement Madhavan, Madhusudan Alexanderian, Alen Saibaba, Arvind K. Waanders, Bart van Bloemen White, Rebekah D. Optimization and Control Numerical Analysis 65M32, 49N45, 62K05, 62F15, 35R30, 65C60 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. |
| title | A control-oriented approach to optimal sensor placement |
| topic | Optimization and Control Numerical Analysis 65M32, 49N45, 62K05, 62F15, 35R30, 65C60 |
| url | https://arxiv.org/abs/2502.15062 |