相关论文: Mean-Field Sparse Jurdjevic--Quinn Control

A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…

We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In…

We consider a nonlinear discrete stochastic control system, and our goal is to design a feedback control policy in order to lead the system to a prespecified state. We adopt a stochastic approximation viewpoint of this problem. It is known…

This paper studies a class of mean-field control (MFC) problems with singular controls under general dynamic state-control-law constraints. We first propose a customized relaxed control formulation to cope with the dynamic mixed constraints…

A Lyapunov-based approach for the trajectory generation of an $N$-dimensional Schr{\"o}dinger equation in whole $\RR^N$ is proposed. For the case of a quantum particle in an $N$-dimensional decaying potential the convergence is precisely…

Let a control system and a target be given on an open subset of an Euclidean space. The existence of a Control Lyapunov Function - namely a positive definite, semiconcave, solution of the Hamilton-Jacobi inequality corresponding to the…

We present a generalized dynamical mean-field approach for the nonequilibrium physics of a strongly correlated system in the presence of a time-dependent external field. The Keldysh Green's function formalism is used to study the…

Controller design for nonlinear systems with Control Lyapunov Function (CLF) based quadratic programs has recently been successfully applied to a diverse set of difficult control tasks. These existing formulations do not address the gap…

In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…

In this article, we provide an original systematic global-in-time analysis of mean field type control problems on $\mathbb{R}^n$ with generic cost functionals by the modified approach but not the same, firstly proposed in [7], as the…

Stochastic convergence of discrete time Markov processes has been analysed based on a dual Lyapunov approach. Using some existing results on ergodic theory of Markov processes, it has been shown that existence of a properly subinvariant…

This article is concerned with an optimal control problem derived by mean-field forward-backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are…

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…

This paper introduces a system of stochastic differential equations (SDE) of mean-field type that models pedestrian motion. The system lets the pedestrians spend time at, and move along, walls, by means of sticky boundaries and boundary…

We consider an optimal control problem for piecewise deterministic Markov processes (PDMPs) on a bounded state space. The control problem under study is very general: a pair of controls acts continuously on the deterministic flow and on the…

Using a nonlocal macroscopic LWR-type traffic flow model, we present an approach to control the nonlocal velocity towards a given equilibrium velocity. Therefore, we present a Lyapunov function measuring the $L^2$ distance between these…

In this paper, we study a linear-quadratic optimal control problem for mean-field stochastic differential equations driven by a Poisson random martingale measure and a multidimensional Brownian motion. Firstly, the existence and uniqueness…

We propose a PDE-based accelerated gradient algorithm for optimal feedback controls of McKean-Vlasov dynamics that involve mean-field interactions both in the state and action. The method exploits a forward-backward splitting approach and…

We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…

Mean-field stochastic differential equations, also called McKean--Vlasov equations, are the limiting equations of interacting particle systems with fully symmetric interaction potential. Such systems play an important role in a variety of…