Related papers: Representation of asymptotic values for nonexpansi…
In this paper we study by probabilistic techniques the convergence of the value function for a two-scale, infinite-dimensional, stochastic controlled system as the ratio between the two evolution speeds diverges. The value function is…
For optimal control problems on finite graphs in continuous time, the dynamic programming principle leads to value functions characterized by systems of nonlinear ordinary differential equations. In this paper, we consider the case of…
We show a connection between global unconstrained optimization of a continuous function $f$ and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solution $v$ of the critical Hamilton-Jacobi equation is built…
A linear control system with quadratic cost functional over infinite time horizon is considered without assuming controllability/stabilizability condition and the global integrability condition for the nonhomogeneous term of the state…
We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this…
We study an optimal control problem on infinite time horizon with semimartingale strategies, random coefficients and regime switching. The value function and the optimal strategy can be characterized in terms of three systems of backward…
In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…
We present a fully nonparametric method to estimate the value function, via simulation, in the context of expected infinite-horizon discounted rewards for Markov chains. Estimating such value functions plays an important role in approximate…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…
In the context of the multi-dimensional infinite horizon optimal consumption-investment problem with proportional transaction costs, we provide the first order expansion in small transact costs. Similar to the one-dimensional derivation in…
We consider the scheduling control problem for a family of unitary networks under heavy traffic, with general interarrival and service times, probabilistic routing and infinite horizon discounted linear holding cost. A natural…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
This paper is concerned with a finite-horizon inverse control problem, which has the goal of reconstructing, from observations, the possibly non-convex and non-stationary cost driving the actions of an agent. In this context, we present a…
We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…
We study a stochastic, continuous time model on a finite horizon for a firm that produces a single good. We model the production capacity as an Ito diffusion controlled by a nondecreasing process representing the cumulative investment. The…
We present a stochastic model predictive control framework for nonlinear systems subject to unbounded process noise with closed-loop guarantees. First, we provide a conceptual shrinking-horizon framework that utilizes general probabilistic…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…