Related papers: Mean-Field Control for Diffusion Aggregation syste…
We discuss the optimal Markovian coupling before an exponential time of the Kolmogorov diffusion, and a class of related stochastic control problems in which the aim is to hit the origin before an exponential time. We provide a scaling…
The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence…
This paper, the second of a two-part series, presents a method for mean-field feedback stabilization of a swarm of agents on a finite state space whose time evolution is modeled as a continuous time Markov chain (CTMC). The resulting…
The Keller-Segel model is a system of partial differential equations that describes the movement of cells or organisms in response to chemical signals, a phenomenon known as chemotaxis. In this study, we analyze a doubly parabolic…
We establish an explicit rate of convergence for some systems of mean-field interacting diffusions with logistic binary branching towards the solutions of nonlinear evolution equations with non-local self-diffusion and logistic mass growth,…
We formulate and compute a class of mean-field information dynamics for reaction-diffusion equations. Given a class of nonlinear reaction-diffusion equations and entropy type Lyapunov functionals, we study their gradient flows formulations…
We develop a limit theory for controlled mean field stochastic partial differential equations in a variational framework. More precisely, we prove existence results for mean field limits and particle approximations, and we establish a…
In this article, we apply a probabilistic approach to study general mean field type control (MFTC) problems with jump-diffusions, and give the first global-in-time solution. We allow the drift coefficient $b$ and the diffusion coefficient…
Optimal control of large particle systems with collective dynamics by few agents is a subject of high practical importance (e.g. in evacuation dynamics), but still limited mathematical basis. In particular the transition from discrete…
In this paper, the finite horizon asymmetric information linear quadratic (LQ) control problem is investigated for a discrete-time mean field system. Different from previous works, multiple controllers with different information sets are…
The mean-field limit of interacting diffusions without exchangeability, caused by weighted interactions and non-i.i.d. initial values, are investigated. The weights could be signed and unbounded. The result applies to a large class of…
Schr\"{o}dinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process whose terminal distribution coincides with a pre-specified target distribution. We…
Interacting particle systems are known for their ability to generate large-scale self-organized structures from simple local interaction rules between each agent and its neighbors. In addition to studying their emergent behavior, a main…
Ensemble control offers rich and diverse opportunities in mathematical systems theory. In this paper, we present a new paradigm of ensemble control, referred to as distributional control, for ensemble systems. We shift the focus from…
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…
Controlling complex physics systems is important in diverse domains. While diffusion-based methods have demonstrated advantages over classical model-based approaches and myopic sequential learning methods in achieving global trajectory…
The mean-field game system is treated as an Euler Lagrange system corresponding to an optimal control problem governed by Fokker-Planck equation.
Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered…
In this manuscript, we study a class of linear-quadratic (LQ) mean field control problems with a common noise and their corresponding $N$-particle systems. The mean field control problems considered are not standard LQ mean field control…
This paper establishes an indirect approximation theorem for the most probable transition pathway of a stochastic interacting particle system in the mean-field framework. This paper studied the problem of indirect approximation of the most…