English
Related papers

Related papers: Linear-quadratic control for mean-field backward s…

200 papers

The finite horizon $H_2/H_\infty$ control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, we derive a mean-field stochastic bounded real lemma (SBRL). Secondly, a sufficient condition for the…

Optimization and Control · Mathematics 2016-07-05 Zhang Weihai , Ma Limin

We study a linear quadratic optimal control problem with stochastic coefficients and a terminal state constraint, which may be in force merely on a set with positive, but not necessarily full probability. Under such a partial terminal…

Optimization and Control · Mathematics 2017-11-15 Peter Bank , Moritz Voß

In the present paper we discuss a new type of mean-field coupled forward-backward stochastic differential equations (MFFBSDEs). The novelty consists in the fact that the coefficients of both the forward as well as the backward SDEs depend…

Probability · Mathematics 2023-07-27 Rainer Buckdahn , Juan Li , Junsong Li , Chuanzhi Xing

In this paper we present a novel sampling-based numerical scheme designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear…

Systems and Control · Computer Science 2020-06-18 Ioannis Exarchos , Evangelos A. Theodorou

We study a finite-dimensional continuous-time optimal control problem on finite horizon for a controlled diffusion driven by Brownian motion, in the linear-quadratic case. We admit stochastic coefficients, possibly depending on an…

Optimization and Control · Mathematics 2016-09-19 Fulvia Confortola , Marco Fuhrman , Giuseppina Guatteri , Gianmario Tessitore

In this work, we focus on an infinite horizon mean-field linear-quadratic stochastic control problem with jumps. Firstly, the infinite horizon linear mean-field stochastic differential equations and backward stochastic differential…

Optimization and Control · Mathematics 2023-11-14 Qingmeng Wei , Yaqi Xu , Zhiyong Yu

In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…

Optimization and Control · Mathematics 2024-01-17 Yuhang Li , Yuecai Han

This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs), where the coefficients of the backward system and the cost functionals are deterministic, and the control domain is convex. Necessary and…

Optimization and Control · Mathematics 2019-04-18 Yueyang Zheng , Jingtao Shi

A modified Deep BSDE (backward differential equation) learning method with measurability loss, called Deep BSDE-ML method, is introduced in this paper to solve a kind of linear decoupled forward-backward stochastic differential equations…

Optimization and Control · Mathematics 2022-01-06 Yutian Wang , Yuan-Hua Ni

In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a…

Optimization and Control · Mathematics 2021-06-23 Shaolin Ji , Shige Peng , Ying Peng , Xichuan Zhang

In this paper, we study the optimal control system driven by stochastic differential equations (SDEs) of mean-field type, in which the control variable has two components, the first being absolutely continuous and the second singular. On…

Optimization and Control · Mathematics 2012-11-02 Liangquan Zhang

In this paper we introduce a new kind of Backward Stochastic Differential Equations, called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness and regularity of solution to…

Probability · Mathematics 2007-07-31 Marco Fuhrman , Ying Hu , Gianmario Tessitore

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that…

Probability · Mathematics 2015-12-01 Huyên Pham , Xiaoli Wei

A mixed linear quadratic (MLQ, for short) optimal control problem is considered. The controlled stochastic system consists of two diffusion processes which are in different time horizons. There are two control actions: a standard control…

Optimization and Control · Mathematics 2012-12-05 Jianhui Huang , Xun Li , Jiongmin Yong

In this paper, we study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal sate constraints. Applying the terminal perturbation method and Ekeland's…

Optimization and Control · Mathematics 2012-11-20 Shaolin Ji , Qingmeng Wei , Xiumin Zhang

We formulate and solve an optimal control problem with cooperative, mean-field coupled linear-quadratic subsystems and additional risk-aware costs depending on the covariance and skew of the disturbance. This problem quantifies the…

Systems and Control · Electrical Eng. & Systems 2024-06-11 Dhairya Patel , Margaret Chapman

We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…

Optimization and Control · Mathematics 2019-08-07 Marco Fuhrman , Marie-Amélie Morlais

This paper studies a linear-quadratic mean-field game of stochastic large-population system, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equation. Different from the…

Optimization and Control · Mathematics 2024-12-02 Yu Si , Jingtao Shi

The objective of the present paper is to investigate the solution of fully coupled mean-field forward-backward stochastic differential equations (FBSDEs in short) and to study the stochastic control problems of mean-field type as well as…

Optimization and Control · Mathematics 2012-07-19 Ruimin Xu , Liangquan Zhang

This paper is devoted to an optimal control problem of fully coupled forward-backward stochastic differential equations driven by sub-diffusion, whose solutions are not Markov processes. The stochastic maximum principle is obtained, where…

Optimization and Control · Mathematics 2025-03-11 Chenhui Hao , Jingtao Shi , Shuaiqi Zhang