English
Related papers

Related papers: The mean-field control problem for heterogeneous f…

200 papers

In this article, we study the global-in-time well-posedness of second order mean field games (MFGs) with both nonlinear drift functions simultaneously depending on the state, distribution and control variables, and the diffusion term…

Optimization and Control · Mathematics 2025-03-24 Alain Bensoussan , Ziyu Huang , Shanjian Tang , Sheung Chi Phillip Yam

A Linear-quadratic optimal control problem is considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which turns out to be a linear mean-field…

Optimization and Control · Mathematics 2011-10-10 Jiongmin Yong

Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…

Analysis of PDEs · Mathematics 2020-06-16 Ugur G. Abdulla , Evan Cosgrove

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…

Adaptation and Self-Organizing Systems · Physics 2018-06-22 Piyush Grover , Kaivalya Bakshi , Evangelos A. Theodorou

Multi-agent reinforcement learning methods have shown remarkable potential in solving complex multi-agent problems but mostly lack theoretical guarantees. Recently, mean field control and mean field games have been established as a…

Machine Learning · Computer Science 2021-12-20 Kai Cui , Anam Tahir , Mark Sinzger , Heinz Koeppl

In this paper, we study an optimal control problem of a mean-field forward-backward stochastic system with random jumps in progressive structure, where both regular and singular controls are considered in our formula. In virtue of the…

Optimization and Control · Mathematics 2023-05-30 Tian Chen , Kai Du , Zongyuan Huang , Zhen Wu

This paper studies optimal control and stabilization problems for continuous-time mean-field systems with input delay, which are the fundamental development of control and stabilization problems for mean-field systems. There are two main…

Optimization and Control · Mathematics 2020-10-19 Xiao Ma , Qingyuan Qi , Xun Li , Huanshui Zhang

In this article, by using several new crucial {\it a priori} estimates which are still absent in the literature, we provide a comprehensive resolution of the first order generic mean field type control problems and also establish the…

Optimization and Control · Mathematics 2023-09-18 Alain Bensoussan , Tak Kwong Wong , Sheung Chi Phillip Yam , Hongwei Yuan

We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…

Probability · Mathematics 2008-12-20 Seid Bahlali

In this paper, we study a class of linear-quadratic (LQ) mean-field games in which the individual control process is constrained in a closed convex subset $\Gamma$ of full space $\mathbb{R}^m$. The decentralized strategies and consistency…

Optimization and Control · Mathematics 2016-10-20 Ying Hu , Huang Jianhui , Xun Li

A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population.…

Optimization and Control · Mathematics 2021-06-15 Giacomo Albi , Stefano Almi , Marco Morandotti , Francesco Solombrino

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

In this paper, we study a class of infinite horizon fully coupled McKean-Vlasov forward-backward stochastic differential equations (FBSDEs). We propose a generalized monotonicity condition involving two flexible functions. Under this…

Optimization and Control · Mathematics 2024-03-28 Tianjiao Hua , Peng Luo

In this paper, we study a delayed forward-backward stochastic control system in which all the coefficients depend on the state and control terms, and the control domain is not necessarily convex. A global stochastic maximum principle is…

Optimization and Control · Mathematics 2026-01-21 Feng Li

In this paper, we analyze mean-field game modulated by finite states markov chains. We first develop a sufficient stochastic maximum principle for the optimal control of a Markov-modulated stochastic differential equation (SDE) of…

Optimization and Control · Mathematics 2014-05-22 Yongming Tai

This paper studies a robust stochastic control problem with a monotone mean-variance cost functional and random coefficients. The main technique is to find the saddle point through two backward stochastic differential equations (BSDEs) with…

Optimization and Control · Mathematics 2024-08-19 Yuyang Chen , Tianjiao Hua , Peng Luo

This article introduces and solves a general class of fully coupled forward-backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different…

Probability · Mathematics 2026-05-01 Matteo Casserini , Gechun Liang

In this paper, we examine the stationary relaxed singular control problem within a multi-dimensional framework for a single agent, as well as its mean field game equivalent. We demonstrate that optimal relaxed controls exist for two problem…

Optimization and Control · Mathematics 2025-06-04 Asaf Cohen , Chuhao Sun

In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward…

Probability · Mathematics 2007-11-21 Rainer Buckdahn , Juan Li , Shige Peng

We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak…

Analysis of PDEs · Mathematics 2015-04-07 Yves Achdou , Mathieu Lauriere