Shortest-path recovery from signature with an optimal control approach Article Swipe

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Marco Rauscher , Alessandro Scagliotti , F. Patrı́cio ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.1007/s00498-024-00402-8

In this paper, we consider the signature-to-path reconstruction problem from the control-theoretic perspective. Namely, we design an optimal control problem whose solution leads to the minimal-length path that generates a given signature. In order to do that, we minimize a cost functional consisting of two competing terms, i.e., a weighted final-time cost combined with the $$L^2$$ -norm squared of the controls. Moreover, we can show that, by taking the limit to infinity of the parameter that tunes the final-time cost, the problem $$\Gamma $$ -converges to the problem of finding a sub-Riemannian geodesic connecting two signatures. Finally, we provide an alternative reformulation of the latter problem, which is particularly suitable for the numerical implementation.

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Mathematics Path (computing) Shortest path problem Signature (topology) Control (management) Mathematical optimization Control theory (sociology) Algorithm Computer science Artificial intelligence Combinatorics Computer network Geometry Graph

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Type: article
Language: en
Landing Page: https://doi.org/10.1007/s00498-024-00402-8
OA Status: hybrid
Cited By: 1
References: 22
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DOI: https://doi.org/10.1007/s00498-024-00402-8

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Title: Shortest-path recovery from signature with an optimal control approach

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Language: en

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Publication year: 2024

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Publication date: 2024-10-14

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Authors: Marco Rauscher, Alessandro Scagliotti, F. Patrı́cio

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Landing page: https://doi.org/10.1007/s00498-024-00402-8

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Concepts: Mathematics, Path (computing), Shortest path problem, Signature (topology), Control (management), Mathematical optimization, Control theory (sociology), Algorithm, Computer science, Artificial intelligence, Combinatorics, Computer network, Geometry, Graph

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Cited by: 1

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abstract_inverted_index.implementation.	125
abstract_inverted_index.control-theoretic	12
abstract_inverted_index.signature-to-path	7
abstract_inverted_index.<mml:mi>L</mml:mi>	60
abstract_inverted_index.<mml:mn>2</mml:mn>	61
abstract_inverted_index.<mml:mi>Γ</mml:mi>	94
abstract_inverted_index.xmlns:mml="http://www.w3.org/1998/Math/MathML">	58, 93
cited_by_percentile_year.max	95
cited_by_percentile_year.min	91
corresponding_author_ids	https://openalex.org/A5093081510
countries_distinct_count	1
institutions_distinct_count	3
corresponding_institution_ids	https://openalex.org/I62916508
citation_normalized_percentile.value	0.77982386
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False