相关论文: On the Dynamic Programming approach to economic mo…

In this manuscript we consider optimal control problems of stochastic differential equations with delays in the state and in the control. First, we prove an equivalent Markovian reformulation on Hilbert spaces of the state equation. Then,…

We consider a class of optimal control problems of stochastic delay differential equations (SDDE) that arise in connection with optimal advertising under uncertainty for the introduction of a new product to the market, generalizing…

This paper, which is the natural continuation of a previous paper by the same authors, studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes…

In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…

This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution…

In this paper, we study the delayed stochastic recursive optimal control problem with a non-Lipschitz generator, in which both the dynamics of the control system and the recursive cost functional depend on the past path segment of the state…

We study a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to…

In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraints for the cost function where the cost function is described by the solution of one reflected backward stochastic differential…

In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…

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 present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear…

In this article, a class of optimal control problems of differential equations with delays are investigated for which the associated Hamilton-Jacobi-Bellman (HJB) equations are nonlinear partial differential equations with delays. This type…

This survey collects, within a unified framework, various results (primarily by the authors themselves) on the use of Deterministic Infinite-Dimensional Optimal Control Theory to address applied economic models. The main aim is to…

In this note, we study a class of indefinite stochastic McKean-Vlasov linear-quadratic (LQ in short) control problem under the control taking nonnegative values. In contrast to the conventional issue, both the classical dynamic programming…

Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…

Recent work [Ran22] formulated a class of optimal control problems involving positive linear systems, linear stage costs, and elementwise constraints on control. It was shown that the problem admits linear optimal cost and the associated…

We analyze an optimal stopping problem with a constraint on the expected cost. When the reward function and cost function are Lipschitz continuous in state variable, we show that the value of such an optimal stopping problem is a continuous…

Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a…

This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB)…

In this paper, we study backward doubly stochastic recursive optimal control problem where the cost function is described by the solution of a backward doubly stochastic differential equation. We give the dynamical programming principle for…