Related papers: Vanishing viscosity in mean-field optimal control
We consider the Cauchy problem for a strictly hyperbolic, $n\times n$ system in one space dimension: $u_t+A(u)u_x=0$, assuming that the initial data has small total variation. We show that the solutions of the viscous approximations…
A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the…
We provide a new version of the Tikhonov theorem for both two-scale forward systems and also two-scale forward-backward systems of stochastic differential equations, which also covers the McKean-Vlasov case. Differently from what is usually…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle…
The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially important to include time-varying parameters that impact viral epidemic-like…
In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…
This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls…
We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon pro\-blems, and allow notably some coefficients to be stochastic. Extension to…
In this paper, we study the existence of an optimal strategy for the stochastic control of diffusion in general case and a saddle-point for zero-sum stochastic differential games. The problem is formulated as an extended BSDE with…
We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a large population of particles (players) in mean-field…
We prove Lipschitz continuity of viscosity solutions to a class of two-phase free boundary problems governed by fully nonlinear operators.
Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
In this paper we prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a finite dimensional stochastic differential equation, driven by a multidimensional Wiener process. We drop the usual…
In this paper we propose and study a spatial diffusion model for the control of anthracnose disease in a bounded domain. The model is a generalization of the one previously developed in [14]. We use the model to simulate two different types…
Although the mean-variance control was initially formulated for financial portfolio management problems in which one wants to maximize expected return and control the risk, our motivations also stem from highway vehicle platoon controls…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…