Fully Coupled Nonlinear FBS△Es: Solvability and LQ Control Insights

Zhipeng Niu; Qingxin Meng; Xun Li; Maoling Tao

doi:10.1016/j.automatica.2025.112601

Fully Coupled Nonlinear FBS△Es: Solvability and LQ Control Insights

Zhipeng Niu
, Qingxin Meng
, Xun Li
, Maoling Tao

Research output: Journal article publication › Journal article › Academic research › peer-review

1 Citation (Scopus)

Abstract

In this paper, a class of fully coupled nonlinear forward–backward stochastic difference equations (FBS△Es) is proposed and the existence of solutions is proved based on a linear-quadratic (LQ) optimal control problem. Inspired from the solvability studies of various forward–backward stochastic differential equations (FBSDEs), the dominant-monotone framework is discretized and a continuum approach is used to prove the unique solvability of the fully coupled FBS△Es and to obtain a pair of estimates on the solutions, and finally, the conclusions are applied to the related LQ problem.

Original language	English
Article number	112601
Pages (from-to)	1-13
Number of pages	13
Journal	Automatica
Volume	183
Issue number	112601
DOIs	https://doi.org/10.1016/j.automatica.2025.112601
Publication status	Published - Jan 2026

Keywords

Continuation method
Domination-monotonicity conditions
Forward–backward stochastic difference equations
Hamiltonian system
LQ problem

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

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10.1016/j.automatica.2025.112601Licence: Other

http://hdl.handle.net/10397/119969

Cite this

@article{361a02b42aa74388b4905eb6993f2d2a,

title = "Fully Coupled Nonlinear FBS△Es: Solvability and LQ Control Insights",

abstract = "In this paper, a class of fully coupled nonlinear forward{\textendash}backward stochastic difference equations (FBS△Es) is proposed and the existence of solutions is proved based on a linear-quadratic (LQ) optimal control problem. Inspired from the solvability studies of various forward{\textendash}backward stochastic differential equations (FBSDEs), the dominant-monotone framework is discretized and a continuum approach is used to prove the unique solvability of the fully coupled FBS△Es and to obtain a pair of estimates on the solutions, and finally, the conclusions are applied to the related LQ problem.",

keywords = "Continuation method, Domination-monotonicity conditions, Forward{\textendash}backward stochastic difference equations, Hamiltonian system, LQ problem",

author = "Zhipeng Niu and Qingxin Meng and Xun Li and Maoling Tao",

note = "Publisher Copyright: {\textcopyright} 2025",

year = "2026",

month = jan,

doi = "10.1016/j.automatica.2025.112601",

language = "English",

volume = "183",

pages = "1--13",

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T1 - Fully Coupled Nonlinear FBS△Es: Solvability and LQ Control Insights

AU - Niu, Zhipeng

AU - Meng, Qingxin

AU - Li, Xun

AU - Tao, Maoling

PY - 2026/1

Y1 - 2026/1

N2 - In this paper, a class of fully coupled nonlinear forward–backward stochastic difference equations (FBS△Es) is proposed and the existence of solutions is proved based on a linear-quadratic (LQ) optimal control problem. Inspired from the solvability studies of various forward–backward stochastic differential equations (FBSDEs), the dominant-monotone framework is discretized and a continuum approach is used to prove the unique solvability of the fully coupled FBS△Es and to obtain a pair of estimates on the solutions, and finally, the conclusions are applied to the related LQ problem.

AB - In this paper, a class of fully coupled nonlinear forward–backward stochastic difference equations (FBS△Es) is proposed and the existence of solutions is proved based on a linear-quadratic (LQ) optimal control problem. Inspired from the solvability studies of various forward–backward stochastic differential equations (FBSDEs), the dominant-monotone framework is discretized and a continuum approach is used to prove the unique solvability of the fully coupled FBS△Es and to obtain a pair of estimates on the solutions, and finally, the conclusions are applied to the related LQ problem.

KW - Continuation method

KW - Domination-monotonicity conditions

KW - Forward–backward stochastic difference equations

KW - Hamiltonian system

KW - LQ problem

UR - https://www.scopus.com/pages/publications/105016822872

U2 - 10.1016/j.automatica.2025.112601

DO - 10.1016/j.automatica.2025.112601

M3 - Journal article

SN - 0005-1098

VL - 183

SP - 1

EP - 13

JO - Automatica

JF - Automatica

IS - 112601

M1 - 112601

ER -

Fully Coupled Nonlinear FBS△Es: Solvability and LQ Control Insights

Abstract

Keywords

ASJC Scopus subject areas

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