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In this paper, we mainly focus on solving high-dimensional stochastic Hamiltonian systems with boundary condition, which is essentially a Forward Backward Stochastic Differential Equation (FBSDE in short), and propose a novel method from…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…
We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…
We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is…
In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an…
In this paper, the stochastic verification theorems for stochastic control problems of reflected forward-backward stochastic differential equations are studied. We carry out the work within the frameworks of classical and viscosity…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented.…
A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of…
In this paper, we investigate a decentralized control problem with nested subsystems, which is a general model for one-directional communication amongst many subsystems. The noises in our dynamics are modelled as uncertain variables which…
In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated…
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
Stochastic differential equations (sdes) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes…
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…
We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution.…
This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely…