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We study a multi-agent mean field type control problem in discrete time where the agents aim to find a socially optimal strategy and where the state and action spaces for the agents are assumed to be continuous. The agents are only weakly…

Optimization and Control · Mathematics 2025-04-01 Erhan Bayraktar , Nicole Bauerle , Ali Devran Kara

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

We study normal approximations for a class of discrete-time occupancy processes, namely, Markov chains with transition kernels of product Bernoulli form. This class encompasses numerous models which appear in the complex networks…

Probability · Mathematics 2018-11-13 Liam Hodgkinson , Ross McVinish , Philip K. Pollett

In Mean Field Games of Controls, the dynamics of the single agent is influenced not only by the distribution of the agents, as in the classical theory, but also by the distribution of their optimal strategies. In this paper, we study…

Analysis of PDEs · Mathematics 2023-02-01 Fabio Camilli , Claudio Marchi

This work presents a novel, inference-based approach to the distributed and cooperative flocking control of aerial robot swarms. The proposed method stems from the Unmanned Aerial Vehicle (UAV) dynamics by limiting the latent set to the…

Robotics · Computer Science 2023-02-17 Malintha Fernando

Focusing on hybrid diffusion dynamics involving continuous dynamics as well as discrete events, this article investigates the explicit approximations for nonlinear switching diffusion systems modulated by a Markov chain. Different kinds of…

Numerical Analysis · Mathematics 2021-12-08 Hongfu Yang , Xiaoyue Li

We discuss the system of Fokker-Planck and Hamilton-Jacobi-Bellman equations arising from the finite horizon control of McKean-Vlasov dynamics. We give examples of existence and uniqueness results. Finally, we propose some simple models for…

Analysis of PDEs · Mathematics 2015-03-18 Yves Achdou , Mathieu Lauriere

We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight…

Statistics Theory · Mathematics 2024-07-08 Yunbum Kook , Matthew S. Zhang , Sinho Chewi , Murat A. Erdogdu , Mufan Bill Li

We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the…

Disordered Systems and Neural Networks · Physics 2016-08-31 A. Bovier , M. Eckhoff , V. Gayrard , M. Klein

In this paper we are concerned with hitting times of a family of density-dependent Markov chains. A moderate deviation principle of the hitting time is given. The proof of the main theorem relies heavily on moderate deviations of…

Probability · Mathematics 2022-06-15 Yuheng He , Xiaofeng Xue

Model Predictive Control is an extremely effective control method for systems with input and state constraints. Model Predictive Control performance heavily depends on the accuracy of the open-loop prediction. For systems with uncertainty…

Optimization and Control · Mathematics 2022-07-27 Francesco Micheli , John Lygeros

We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type…

Probability · Mathematics 2018-09-07 Salah Eddine Choutri , Hamidou Tembine

We develop an exhaustive study of Markov decision process (MDP) under mean field interaction both on states and actions in the presence of common noise, and when optimization is performed over open-loop controls on infinite horizon. Such…

Optimization and Control · Mathematics 2021-09-10 Médéric Motte , Huyên Pham

We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…

Analysis of PDEs · Mathematics 2020-03-10 Y Achdou , Z Kobeissi

The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…

Optimization and Control · Mathematics 2020-03-11 Yves Achdou , Mathieu Laurière

The maximization of reach-avoid probabilities for stochastic systems is a central topic in the control literature. Yet, the available methods are either restricted to low-dimensional systems or suffer from conservative approximations. To…

Optimization and Control · Mathematics 2026-01-26 Niklas Schmid , Jaeyoun Choi , Oswin So , Chuchu Fan

The aim of this paper is to study the asymptotic behavior of a system of birth and death processes in mean field type interaction in discrete space. We first establish the exponential convergence of the particle system to equilibrium for a…

Probability · Mathematics 2015-10-13 Marie-Noémie Thai

This paper studies the sensitivity analysis of mass-action systems against their diffusion approximations, particularly the dependence on population sizes. As a continuous time Markov chain, a mass-action system can be described by a…

Numerical Analysis · Mathematics 2022-11-10 Yao Li , Yaping Yuan

In this paper, we study the $extended$ mean field control problem, which is a class of McKean-Vlasov stochastic control problem where the state dynamics and the reward functions depend upon the joint (conditional) distribution of the…

Probability · Mathematics 2022-04-06 Mao Fabrice Djete

This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…

Probability · Mathematics 2018-05-07 Zeyu Zheng , Harsha Honnappa , Peter W. Glynn