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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

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

Probability · Mathematics 2020-11-03 Masaaki Fujii

We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modeling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an…

Optimization and Control · Mathematics 2015-06-18 Massimo Fornasier , Benedetto Piccoli , Francesco Rossi

In this paper, we investigate a class of mean field games where the mean field interactions are achieved through the joint (conditional) distribution of the controlled state and the control process. The strategies are of $open\;loop$ type,…

Probability · Mathematics 2021-08-05 Mao Fabrice Djete

We consider the convergence problem in the setting of mean field control with common noise and degenerate idiosyncratic noise. Our main results establish a rate of convergence of the finite-dimensional value functions $V^N$ towards the mean…

Optimization and Control · Mathematics 2025-01-22 Alekos Cecchin , Samuel Daudin , Joe Jackson , Mattia Martini

Many applications involving multi-agent systems require fulfilling safety constraints. Control barrier functions offer a systematic framework to enforce forward invariance of safety sets. Recent work extended this paradigm to mean-field…

Systems and Control · Electrical Eng. & Systems 2026-03-20 Cinzia Tomaselli , Gian Carlo Maffettone , Samy Wu Fung , Levon Nurbekyan , Mario di Bernardo

We consider the control of McKean-Vlasov dynamics whose coefficients have mean field interactions in the state and control. We show that for a class of linear-convex mean field control problems, the unique optimal open-loop control admits…

Optimization and Control · Mathematics 2021-09-27 Christoph Reisinger , Wolfgang Stockinger , Yufei Zhang

In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…

Optimization and Control · Mathematics 2025-12-05 P. Jameson Graber , Kyle Rosengartner

The classical stochastic control problem under partial information can be formulated as a control problem for Zakai equation, whose solution is the unnormalized conditional probability distribution of the state of the system. Zakai equation…

Optimization and Control · Mathematics 2019-09-27 Alain Bensoussan , Sheung Chi Phillip Yam

The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence. As a second main result, a…

Probability · Mathematics 2022-12-15 Benjamin Gess , Rishabh S. Gvalani , Vitalii Konarovskyi

Our work is devoted to the study of Pontryagin's stochastic maximum principle for a mean-field optimal control problem under Peng's $G$-expectation. The dynamics of the controlled state process is given by a stochastic differential equation…

Optimization and Control · Mathematics 2022-11-10 Rainer Buckdahn , Bowen He , Juan Li

We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the…

Probability · Mathematics 2020-11-17 Carlo Orrieri

The paper focuses on mean-field type multi-agent control problems with finite state and action spaces where the dynamics and cost structures are symmetric and homogeneous, and are affected by the distribution of the agents. A standard…

Optimization and Control · Mathematics 2025-07-03 Erhan Bayraktar , Ali D. Kara

In this paper, we study the maximum principle of mean field type control problems when the volatility function depends on the state and its measure and also the control, by using our recently developed method. Our method is to embed the…

Optimization and Control · Mathematics 2023-09-14 Alain Bensoussan , Ziyu Huang , Sheung Chi Phillip Yam

Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control…

Probability · Mathematics 2012-05-07 Amarjit Budhiraja , Arka P. Ghosh

We study mean-field control (MFC) problems with common noise using the control randomisation framework, where we substitute the control process with an independent Poisson point process, controlling its intensity instead. To address the…

Optimization and Control · Mathematics 2024-12-31 Robert Denkert , Idris Kharroubi , Huyên Pham

We study methods for solving stochastic control problems of systems of forward-backward mean-field equations with delay, in finite or infinite horizon. Necessary and sufficient maximum principles under partial information are given. The…

Optimization and Control · Mathematics 2016-10-31 Nacira Agram , Elin Engen Rose

The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…

Mathematical Physics · Physics 2012-12-18 M. Fedele

Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general mean-field…

Probability · Mathematics 2016-08-23 Giulia Di Nunno , Hannes Haferkorn

We study a mean field optimal control problem with general non-Markovian dynamics, including both common noise and jumps. We show that its minimizers are Nash equilibria of an associated mean field game of controls. These types of games are…

Optimization and Control · Mathematics 2025-05-12 Felix Höfer , H. Mete Soner