In this paper we investigate the Hamilton-Jacobi-Bellman (HJB) approach for solving a complex real-world optimal control problem in high dimension. We consider the climbing problem for the European launcher Ariane V: The launcher has to reach the Geostationary Transfer Orbit with minimal propellant consumption under state/control constraints. In order to circumvent the well-known curse of dimen...

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...

A bstract . We study the ergodic control problem of switching diffusions representing a typical hybrid system that arises in numerous applications such as fault-tolerant control systems, flexible manufacturing systems, etc. Under fairly general conditions, we establish the existence of a stable, nonrandomized Markov policy which almost surely minimizes the pathwise long-run average cost. We the...

We give a short introduction to the stochastic calculus for Itô-Lévy processes, and review brie‡y the two main methods of optimal control of stochastic systems described by such processes, namely: (i) Dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equation (ii) The stochastic maximum principle and its associated adjoint backward stochastic di¤erential equation (BSDE). The two methods...

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 near-monotonicity, and show that there always exists a solution to the risk-sensitive Hamilton–Jacobi–Bellman (HJB) equation, and that any minimizer in the Hamiltonian is op...

This paper studies the optimal investment problem of utility maximization with taxes, dividends and transaction costs under the constant elasticity of variance (CEV) model. The Hamilton-Jacobi-Bellman (HJB) equation associated with the optimization problem is established via stochastic control approach. Applying power transform and variable change technique, we obtain explicit solutions for the...

over the admissible controls U . Both g and κ · u (u ∈ U) may take positive and negative values. This paper studies the corresponding dynamic programming equation (DPE), a second-order degenerate elliptic partial differential equation of HJB-type with a state constraint boundary condition. Under the controllability condition GU = R and the finiteness of H(q) = supu∈U1{−Gu · q− κ · u}, q ∈ R , w...

Phophodiesterase (PDE) isoenzyme profiles of human cell preparations and tissues have been analysed by a semiquantitative method using selective PDE inhibitors and activators. Neutrophils, eosinophils and monocytes contain PDE IV exclusively. Lymphocytes, alveolar macrophages and endothelial cells contain PDE IV and PDE III, and in addition, PDE I is measured in macrophages and PDE II in endoth...

We consider an ergodic harvesting problem with model ambiguity that arises from biology. To account for the ambiguity, is constructed as a stochastic game two players: decision maker (DM) chooses “best” policy, and adverse player “worst” probability measure. The main result establishing optimal strategy (also referred to control) of DM showing it threshold policy. payoff are obtained by solving...

In rod outer segments the light activation of cGMP phosphodiesterase (PDE alpha beta gamma 2) is accomplished by removal of the gamma inhibitory subunit (PDE gamma) from the PDE alpha beta catalytic subunits. A light activation of the inositol signaling pathway also occurs, but there is little information linking these two signal transduction pathways. Here we report that protein kinase C (PKC)...