相关论文: Deep Learning Methods for Mean Field Control Probl…

Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align…

This paper is concerned with the partial information optimal control problem of mean-field type under partial observation, where the system is given by a controlled mean-field forward-backward stochastic differential equation with…

We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…

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…

Mathematical mean-field approaches have been used in many fields, not only in Physics and Chemistry, but also recently in Finance, Economics, and Game Theory. In this paper we will study a new special mean-field problem in a purely…

We present a theory of optimal control for McKean-Vlasov stochastic differential equations with infinite time horizon and discounted gain functional. We first establish the well-posedness of the state equation and of the associated control…

We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach,…

In this paper, an open problem is solved, for the stochastic optimal control problem with delay where the control domain is nonconvex and the diffusion term contains both control and its delayed term. Inspired by previous results by \O…

Control of distributed parameter systems affected by delays is a challenging task, particularly when the delays depend on spatial variables. The idea of integrating analytical control theory with learning-based control within a unified…

Time delays are ubiquitous in industrial processes, and they must be accounted for when designing control algorithms because they have a significant effect on the process dynamics. Therefore, in this work, we propose a simultaneous approach…

In the present paper we discuss a new type of mean-field coupled forward-backward stochastic differential equations (MFFBSDEs). The novelty consists in the fact that the coefficients of both the forward as well as the backward SDEs depend…

The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the…

This paper presents a Newton-based stochastic extremum-seeking control method for real-time optimization in multi-input systems with distinct input delays. It combines predictor-based feedback and Hessian inverse estimation via stochastic…

In this paper, we propose a new methodology for state constrained stochastic optimal control (SOC) problems. The solution is based on past work in solving SOC problems using forward-backward stochastic differential equations (FBSDE). Our…

In this paper, we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional, with two controllers-one can choose only deterministic time functions, called the deterministic controller, while the other…

In this paper, we study the optimal control system driven by stochastic differential equations (SDEs) of mean-field type, in which the control variable has two components, the first being absolutely continuous and the second singular. On…

A Linear-quadratic optimal control problem is considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which turns out to be a linear mean-field…

We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state…

This paper considers the problem of partially observed optimal control for forward stochastic systems which are driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field…

This paper addresses the design and analysis of a multivariable gradient-based stochastic extremum-seeking control method for multi-input systems with arbitrary input delays. The approach accommodates systems with distinct time delays…