Shortest-Path Recovery From Signature With an Optimal Control Approach

MCML Authors

Alessandro Scagliotti

→ Group Massimo Fornasier
 Applied Numerical Analysis

Abstract

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 -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 -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.

article

---

Mathematics of Control, Signals, and Systems

37. Jun. 2025.

---

Authors

M. Rauscher • A. Scagliotti • F. Pagginelli Patricio

---

Links

DOI

---

Research Area

 A2 | Mathematical Foundations