Related papers: Optimal control for stochastic nonlinear Schroding…
High-dimensional stochastic optimal control (SOC) becomes harder with longer planning horizons: existing methods scale linearly in the horizon $T$, with performance often deteriorating exponentially. We overcome these limitations for a…
We study a two-dimensional stochastic differential equation that has a unique weak solution but no strong solution. We show that this SDE shares notable properties with Tsirelson's example of a one-dimensional SDE with no strong solution.…
In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a…
In this paper, we first investigate the global existence of a solution for the stochastic fractional nonlinear Schr\"odinger equation with radially symmetric initial data in a suitable energy space $H^{\alpha}$. We then show that the…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…
The control-affine Schr\"odinger bridge concerns with a stochastic optimal control problem. Its solution is a controlled evolution of joint state probability density subject to a control-affine It\^o diffusion with a given deadline…
We present a set-oriented graph-based computational framework for continuous-time optimal transport over nonlinear dynamical systems. We recover provably optimal control laws for steering a given initial distribution in phase space to a…
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…
We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
We present a brief overview on the existence/nonexistence of standing waves for the NonLinear Schr\"odinger and the NonLinear Dirac Equations (NLSE/NLDE) on metric graphs with localized nonlinearity. We first focus on the NLSE, both in the…
A novel stochastic fluid model is proposed with non-ideal structure factor consistent with compressibility, and adjustable transport coefficients. This Stochastic Hard Sphere Dynamics (SHSD) algorithm is a modification of the Direct…
We show that the continuous-time gradient descent in Rn can be viewed as an optimal controlled evolution for a suitable action functional; a similar result holds for stochastic gradient descent. We then provide an analogous characterization…
We consider policy gradient methods for stochastic optimal control problem in continuous time. In particular, we analyze the gradient flow for the control, viewed as a continuous time limit of the policy gradient method. We prove the global…
In this paper we present a novel sampling-based numerical scheme designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear…
Semilinear parabolic systems with bi-linear nonlinearities cover a lot of applications and their optimal control leads to relatively simple optimality conditions. An example is the incompressible Navier-Stokes system for homogeneous fluids,…
We investigate a hierarchical control problem for a one-dimensional Stefan system with localized distributed controls. The setting combines a Stackelberg strategy with a Nash equilibrium among multiple followers, yielding a multi-objective…
In this paper we study a Pontryagin type stochastic maximum principle for the optimal control of a system, where the state dynamics satisfy a stochastic partial differential equation (SPDE) driven by a two-parameter (time-space) Brownian…