Related papers: Asymptotic problems in optimal control with a vani…
We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the…
We investigate conditions of optimality for an infinite horizon control problem and consider their correspondence with the value function. Assuming Lipschitz continuity of the value function, we prove that sensitivity relations plus the…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely…
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal…
In this paper, we consider a linear quadratic (LQ) optimal control problem in both finite and infinite dimensions. We derive an asymptotic expansion of the value function as the fixed time horizon T tends to infinity. The leading term in…
This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with constant coefficients. It is proved that the non-emptiness of the admissible control set for all initial state is…
We adopt an optimal-control framework for addressing the undiscounted infinite-horizon discrete-time restless $N$-armed bandit problem. Unlike most studies that rely on constructing policies based on the relaxed single-armed Markov Decision…
We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to…
The mathematical framework of hybrid system is a recent and general tool to treat control systems involving control action of heterogeneous nature. In this paper, we construct and test a semi-Lagrangian numerical scheme for solving the…
In this paper we deal with infinite horizon optimal control problems. Basing on weak variations in an extremal problem in weighted function spaces we prove necessary conditions in form of the adjoint equation and a variational inequality.…
This paper revisits the bandit problem in the Bayesian setting. The Bayesian approach formulates the bandit problem as an optimization problem, and the goal is to find the optimal policy which minimizes the Bayesian regret. One of the main…
In the paper we consider the infinite horizon control problems on the interval with free right-hand endpoint. We obtain the necessary conditions of strict optimality. The method of the proof actually follows the classic paper by Halkin, and…
The aim of the paper is to study an optimal control problem on infinite horizon for an infinite dimensional integro-differential equation with completely monotone kernelskernels, where we assume that the noise enters the system when we…
This paper studies a finite horizon utility maximization problem on excessive consumption under a drawdown constraint. Our control problem is an extension of the one considered in Bahman et al. (2019) to the model with a finite horizon and…
We consider restless multi-armed bandit (RMAB) with a finite horizon and multiple pulls per period. Leveraging the Lagrangian relaxation, we approximate the problem with a collection of single arm problems. We then propose an index-based…
The paper addresses an existence problem for infinite horizon optimal control when the system under control is exponentially stabilizable or stable. Classes of nonlinear control systems for which infinite horizon optimal controls exist are…
In this paper we present explicit bounds for optimal control in a Lagrange problem without end-point constraints. The approach we use is due to Gamkrelidze and is based on the equivalence of the Lagrange problem and a time-optimal problem…
We consider an infinite-horizon optimal control problem with an asymptotic terminal constraint. For the the weakly overtaking criterion and the overtaking criterion, necessary boundary conditions on co-state arcs are deduced, these…
We examine the problem of two-point boundary optimal control of nonlinear systems over finite-horizon time periods with unknown model dynamics by employing reinforcement learning. We use techniques from singular perturbation theory to…