Related papers: An Optimal Control Problem with Terminal Stochasti…
While techniques have been developed for chance constrained stochastic optimal control using sample disturbance data that provide a probabilistic confidence bound for chance constraint satisfaction, far less is known about how to use sample…
We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…
This paper addresses the problem of control synthesis for nonlinear optimal control problems in the presence of state and input constraints. The presented approach relies upon transforming the given problem into an infinite-dimensional…
The Method of Successive Approximations (MSA) is a fixed-point iterative method used to solve stochastic optimal control problems. It is an indirect method based on the conditions derived from the Stochastic Maximum Principle (SMP), an…
We establish central limit theorems for the Sample Average Approximation (SAA) method in discrete-time, finite-horizon stochastic optimal control. Our analysis is based on an abstract limit theorem for stochastic backward recursions, which…
In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping, see for example Karatzas and Shreve [SIAM J. Control Optim. 22 (1984)]. The aim of this…
Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for…
In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a…
We consider a class of stochastic optimal control problems with partial observation, and study their approximation by discrete-time control problems. We establish a convergence result by using weak convergence technique of Kushner and…
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…
The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…
This paper addresses a risk-constrained decentralized stochastic linear-quadratic optimal control problem with one remote controller and one local controller, where the risk constraint is posed on the cumulative state weighted variance in…
Conditions are established under which the optimal control of processes having both absolutely continuous and singular (with respect to time) controls are equivalent to linear programs over a space of measures on the state and control…
The optimal control problem of stochastic systems is commonly solved via robust or scenario-based optimization methods, which are both challenging to scale to long optimization horizons. We cast the optimal control problem of a stochastic…
Approximate methods to solve stochastic optimal control (SOC) problems have received significant interest from researchers in the past decade. Probabilistic inference approaches to SOC have been developed to solve nonlinear quadratic…
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
This paper introduces a drift optimization model of stochastic optimization problems driven by regulated stochastic processes. A broad range of problems across operations research, machine learning, and statistics can be viewed as…