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In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on $\mathbb{R}^{d}\times\mathbb{R}^{d}$ derived from suitable variational…
In this paper, we study the problem of traffic management in highways facing stochastic perturbations. To model the macroscopic traffic flow under perturbations, we use cell-transmission model with Markovian capacities. The decision…
We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…
The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an It\^o type stochastic differential equation with control process entering both in the drift and the…
A discretization of an optimal control problem of a stochastic parabolic equation driven by multiplicative noise is analyzed. The state equation is discretized by the continuous piecewise linear element method in space and by the backward…
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…
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…
We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a penalised and smoothed problem and studying convergence of the…
We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…
This paper studies the approximation of optimal control policies by quantized (discretized) policies for a very general class of Markov decision processes (MDPs). The problem is motivated by applications in networked control systems,…
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…
This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational…
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…
We consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
Many discrete-time optimal stopping problems are known to have more tractable limit forms based on a planar Poisson process. Using this tool we find a solution to the optimal stopping problem for i.i.d. sequence of $n$ discrete uniform…
This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization…
This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine…
This study presents the design, discretization and implementation of the continuous-time linear-quadratic model predictive control (CT-LMPC). The control model of the CT-LMPC is parameterized as transfer functions with time delays, and they…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…