Related papers: Randomization method and backward SDEs for optimal…
We address the path-wise control of systems described by a set of nonlinear stochastic differential equations. For this class of systems, we introduce a notion of stochastic relative degree and a change of coordinates which transforms the…
In this paper, we consider a class of stochastic control problems for stochastic differential equations with random coefficients. The control domain need not to be convex but the control process is not allowed to enter in diffusion term.…
Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…
This thesis is concerned with the stochastic filtering problem for a hidden Markov model (HMM) with the white noise observation model. For this filtering problem, we make three types of original contributions: (1) dual controllability…
This work addresses the optimal covariance control problem for stochastic discrete-time linear time-varying systems subject to chance constraints. Covariance steering is a stochastic control problem to steer the system state Gaussian…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
We study a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift. The drift coefficient is assumed to decompose as $b(t,x,a)=b_1(t,x)+b_2(x)b_3(t,a)$, where $b_1$ is bounded and…
Choosing control inputs randomly can result in a reduced expected cost in optimal control problems with stochastic constraints, such as stochastic model predictive control (SMPC). We consider a controller with initial randomization, meaning…
We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular…
Stochastic optimal control with unknown randomness distributions has been studied for a long time, encompassing robust control, distributionally robust control, and adaptive control. We propose a new episodic Bayesian approach that…
System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the…
This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…
Optimal control problems with nonsmooth objectives and nonlinear partial differential equation (PDE) constraints are challenging, mainly because of the underlying nonsmooth and nonconvex structures and the demanding computational cost for…
In this paper, we compare the performance of two scenario-based numerical methods to solve stochastic optimal control problems: scenario trees and particles. The problem consists in finding strategies to control a dynamical system perturbed…
Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…
In this paper we focus on a general type of mean-field stochastic control problem with partial observation, in which the coefficients depend in a non-linear way not only on the state process $X_t$ and its control $u_t$ but also on the…
We consider optimal signalling and control of discrete-time nonlinear partially observable stochastic systems in state space form. In the first part of the paper, we characterize the operational {\it control-coding capacity}, $C_{FB}$ in…
This paper studies a robust stochastic control problem with a monotone mean-variance cost functional and random coefficients. The main technique is to find the saddle point through two backward stochastic differential equations (BSDEs) with…
In this paper we study a class of combined regular and singular stochastic control problems that can be expressed as constrained BSDEs. In the Markovian case, this reduces to a characterization through a PDE with gradient constraint. But…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…