Work

A fully coupled FBSDE framework for optimal orbit steering near an Arneodo-Coullet-Tresser spiral attractor

Year: 2026

Type: article

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.

Source: Communications in Nonlinear Science and Numerical Simulation

DOI: 10.1016/j.cnsns.2026.110319

Author: Dong Feng

Institution: RWTH Aachen University

Language: English

Topic: Chaos control and synchronization

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,710

Funder: China Scholarship Council