Related papers: Mean field type control with congestion
We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…
Here, we consider stationary monotone mean-field games (MFGs) and study the existence of weak solutions. First, we introduce a regularized problem that preserves the monotonicity. Next, using variational inequalities techniques, we prove…
We introduce a new approach to derive mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to…
This paper addresses the existence of equilibria for Mean Field type Control problems of first-order with non-convex action functional. Introducing a relaxed Lagrangian approach on the Wasserstein space to handle the lack of convexity. we…
In this paper, we first prove that the mean-field stochastic linear quadratic (MFSLQ for short) control problem with random coefficients has a unique optimal control and derive a preliminary stochastic maximum principle to characterize this…
We investigate convergence and turnpike properties for linear-quadratic mean field control problems with common noise. Within a unified framework, we analyze a finite-horizon social optimization problem, its mean field control limit, and…
In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of the law and the state of the process. We establish a new…
This paper is concerned with mean-field stochastic linear-quadratic (MF-SLQ, for short) optimal control problems with deterministic coefficients. The notion of weak closed-loop optimal strategy is introduced. It is shown that the open-loop…
The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations.…
This paper considers two types of boundary control problems for linear transport equations. The first one shows that transport solutions on a subdomain of a domain X can be controlled exactly from incoming boundary conditions for X under…
We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle…
An existence result for a class of mean field games of controls is provided. In the considered model, the cost functional to be minimized by each agent involves a price depending at a given time on the controls of all agents and a…
This paper presents an application of mean field control to dynamic production optimization. Both noncooperative and cooperative solutions are considered. We first introduce a market of a large number of agents (firms) with sticky prices…
We introduce a class of robust control problems formulated in min-max form, in which the principal agent is viewed as a central planner facing Nature. The agent's cost is a nonlinear function of all its possible realizations, encompassing…
This paper establishes an equilibrium existence result for a class of Mean Field Games involving Reflected Stochastic Differential Equations. The proof relies on the framework of relaxed controls and martingale problems.
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…
We survey recent results on controlled particle systems. The control aspect introduces new challenges in the discussion of properties and suitable mean field limits. Some of the aspects are highlighted in a detailed discussion of a…
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…
Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the problems is carefully investigated. Both open-loop and closed-loop…
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…