Data-driven stabilisation of unstable periodic orbits of the three-body problem
File(s)
Published version
Author(s)
Brook, Owen
Bramburger, Jason J
Amato, Davide
Fasel, Urban
Type
Journal Article
Abstract
Many different models of the physical world exhibit chaotic dynamics, from fluid flows and chemical reactions to celestial mechanics. The study of the three-body problem (3BP) and its many different families of unstable periodic orbits (UPOs) has provided fundamental insight into chaotic dynamics as far back as the 19th century. The 3BP, a conservative system, is inherently challenging to sample due to its volume-preservation property. In this paper we present an interpretable data-driven approach for the state-dependent control of UPOs in the 3BP, through leveraging the inherent sensitivity of chaos and the local manifold structure. We overcome the sampling challenge by utilising prior knowledge of UPOs and a novel augmentation strategy. This enables sample-efficient discovery of a verifiable and accurate local Poincaré map in as few as 55 data points. We suggest that the Poincaré map is best discovered at a surface of section where the norm of the monodromy matrix, i.e. the local sensitivity to small perturbations, is the smallest. To stabilise the UPOs, we apply small velocity impulses once each period, determined by solving a convex system of linear matrix inequalities based on the linearised map. We constrain the norm of the decision variables used to solve this system, resulting in locally-optimal velocity impulses directed along the local stable manifold. Critically, this behaviour is achieved in a computationally efficient manner. We demonstrate this sample-efficient and low-energy method across several orbit families in the 3BP, with potential applications ranging from robotics and spacecraft control to fluid dynamics.
Date Issued
2025-11-19
Date Acceptance
2025-11-12
Citation
IEEE Access, 2025, 13, pp.199772-199789
ISSN
2169-3536
Publisher
IEEE
Start Page
199772
End Page
199789
Journal / Book Title
IEEE Access
Volume
13
Copyright Statement
© 2025 The Authors. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
License URL
Identifier
10.1109/ACCESS.2025.3634743
Subjects
INDEX TERMS Chaos control
three-body problem
unstable periodic orbit
SINDy
Poincaré map
manifolds
surface of section
conservative systems
Publication Status
Published
Date Publish Online
2025-11-19