Optimal design of sensors via geometric criteria

Ftouhi I, Zuazua Iriondo E (2023)

Publication Language: English

Publication Status: Accepted

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2023

Journal

Journal of Geometric Analysis Springer Verlag (Germany)

Publisher: Journal of Geometric Analysis (JGEA)

Book Volume: 33

Journal Issue: 253

URI: https://link.springer.com/article/10.1007/s12220-023-01301-1

DOI: 10.1007/s12220-023-01301-1

Open Access Link: https://link.springer.com/article/10.1007/s12220-023-01301-1

Abstract

We consider a convex set Ω and look for the optimal convex sensor ω ⊂ Ω of a given measure that minimizes the maximal distance to the points of Ω. This problem can be written as follows

inf{dH(ω,Ω) | |ω|= c and ω ⊂ Ω},

where c ∈ (0, |Ω|), dH being the Hausdorff distance.

We show that the parametrization via the support functions allows us to formulate the geometric optimal shape design problem as an analytic one. By proving a judicious equivalence result, the shape optimization problem is approximated by a simpler minimization of a quadratic function under linear constraints. We then present some numerical results and qualitative properties of the optimal sensors and exhibit an unexpected symmetry breaking phenomenon.

Authors with CRIS profile

Ilias Ftouhi Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

How to cite

APA:

Ftouhi, I., & Zuazua Iriondo, E. (2023). Optimal design of sensors via geometric criteria. Journal of Geometric Analysis, 33(253). https://doi.org/10.1007/s12220-023-01301-1

MLA:

Ftouhi, Ilias, and Enrique Zuazua Iriondo. "Optimal design of sensors via geometric criteria." Journal of Geometric Analysis 33.253 (2023).

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