Abstract In this paper, we consider the stochastic optimal control problem for jump-diffusion models with state constraints. general, value function of such problems is discontinuous viscosity solution associated Hamilton-Jacobi-Bellman (HJB) equation since regularity cannot be guaranteed at boundary constraint. By adapting target theory, obtain an equivalent representation original by means ba...

In this paper we use a reference trajectory computed by a model predictive method to shrink the computational domain where we set the Hamilton-Jacobi Bellman (HJB) equation. Via a reduced-order approach based on proper orthogonal decomposition(POD), this procedure allows for an efficient computation of feedback laws for systems driven by parabolic equations. Some numerical examples illustrate t...

A new fast algorithm for reinforcement learning (RL) in continuous state and action spaces is proposed. Unlike algorithms based on dynamic programming, the proposed algorithm uses neither temporal nor spatial diierencing. Instead, it couples the solution of the Hamilton-Jacobi-Bellman (HJB) partial diierential equation with the structure of the function approximators that are commonly used toge...

Water management in agriculture is a key issue due to the increasing problem of water scarcity worldwide. Based on the recent progress in the dynamic modeling of plant growth in interaction with the water resource, our objective is to study the optimal control problem of crop irrigation. For this purpose, we first describe the LNAS model for sugar beet growth, driving the dynamics of both plant...

The numerical realization of closed loop control for distributed parameter systems is still a significant challenge and in fact infeasible unless specific structural techniques are employed. In this paper we propose the combination of model reduction techniques based on proper orthogonal decomposition (POD) with the numerical treatment of the Hamilton–Jacobi–Bellman (HJB) equation for infinite ...

Hoogendoorn and Bovy (Transportation Research Part B, 2004, 38(7), 571– 592) developed an approach for a pedestrian user-optimal dynamic assignment in continuous time and space. Although their model was proposed for pedestrian traffic, it can also be applied to urban cities. The model is very general, and consists of a conservation law (CL) and a Hamilton-Jacobi-Bellman (HJB) equation that cont...

Abstract. In this paper, we value hydroelectric power plant cash flows under a stochastic control framework, taking into consideration the implication of operational constraints such as ramping and minimum flow rate constraints for the purpose of environmental protection. The power plant valuation problem under a ramping constraint is characterized as a bounded stochastic control problem, resul...

We study the relative value iteration for the ergodic control problem under a nearmonotone running cost structure for a nondegenerate diffusion controlled through its drift. This algorithm takes the form of a quasilinear parabolic Cauchy initial value problem in R. We show that this Cauchy problem stabilizes, or in other words, that the solution of the quasilinear parabolic equation converges f...

This study investigates the optimal switching boundary to a renewable fuel when oil prices exhibit continuous random fluctuations along with occasional discontinuous jumps. In this paper, oil prices are modeled to follow jump diffusion processes. A completeness result is derived. Given that the market is complete the value of a contingent claim is risk neutral expectation of the discounted pay ...

Recently in [8] an ergodic control problem for a class of diffusion processes, constrained to take values in a polyhedral cone, was considered. The main result of that paper was that under appropriate conditions on the model, there is a Markov control for which the infimum of the cost function is attained. In the current work we characterize the value of the ergodic control problem via a suitab...