A fully coupled FBSDE framework for optimal orbit steering near an Arneodo-Coullet-Tresser spiral attractor
- 1Faculty of Civil Engineering, RWTH Aachen University, Mies-van-der-Rohe-Straße 1, Aachen, 52074, Germany
Abstract
This paper develops a fully coupled forward-backward stochastic differential equation (FBSDE) framework for optimal orbit steering near a spiral attractor generated by an Arneodo-Coullet-Tresser-type chaotic oscillator. The central objective is not to suppress chaos by point stabilization, but to preserve the intrinsic orbital geometry of the attractor while reducing stochastic deviations from a prescribed reference orbit segment. To achieve this goal, a stochastic tracking problem is formulated for a noisy controlled ACT system, and the corresponding stochastic maximum principle yields a nonlinear fully coupled FBSDE in which the third backward component enters the active chaotic channel through the optimal feedback law. The resulting model establishes a direct link between spiral chaotic dynamics, stochastic optimal control, and adjoint backward propagation. A compact tensor formulation is provided, together with a variational derivation, a local solvability discussion under structured assumptions, and a decoupling-field interpretation. The framework offers a mathematically coherent and comparatively underexplored route for investigating stochastic orbit steering, random attractor neighborhoods, and control-energy allocation in a spiral chaotic environment.
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BibTeX
@article{feng2026fully,
title = {{A fully coupled FBSDE framework for optimal orbit steering near an Arneodo-Coullet-Tresser spiral attractor}},
author = {Dong Feng},
journal = {Communications in Nonlinear Science and Numerical Simulation},
year = {2026},
month = jun,
doi = {10.1016/j.cnsns.2026.110319},
url = {https://doi.org/10.1016/j.cnsns.2026.110319},
note = {CC BY},
}
RIS
TY - JOUR
TI - A fully coupled FBSDE framework for optimal orbit steering near an Arneodo-Coullet-Tresser spiral attractor
AU - Dong Feng
PY - 2026
DA - 2026/06/08
JO - Communications in Nonlinear Science and Numerical Simulation
DO - 10.1016/j.cnsns.2026.110319
UR - https://doi.org/10.1016/j.cnsns.2026.110319
AB - This paper develops a fully coupled forward-backward stochastic differential equation (FBSDE) framework for optimal orbit steering near a spiral attractor generated by an Arneodo-Coullet-Tresser-type chaotic oscillator. The central objective is not to suppress chaos by point stabilization, but to preserve the intrinsic orbital geometry of the attractor while reducing stochastic deviations from a prescribed reference orbit segment. To achieve this goal, a stochastic tracking problem is formulated for a noisy controlled ACT system, and the corresponding stochastic maximum principle yields a nonlinear fully coupled FBSDE in which the third backward component enters the active chaotic channel through the optimal feedback law. The resulting model establishes a direct link between spiral chaotic dynamics, stochastic optimal control, and adjoint backward propagation. A compact tensor formulation is provided, together with a variational derivation, a local solvability discussion under structured assumptions, and a decoupling-field interpretation. The framework offers a mathematically coherent and comparatively underexplored route for investigating stochastic orbit steering, random attractor neighborhoods, and control-energy allocation in a spiral chaotic environment.
SN - 1007-5704
SN - 1878-7274
ER -