Abstract. The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author et al. [26, 27, 28, 29, 30]. Necessary and s...

In this work, an explicitly task-oriented approach to the active vision problem is presented. The system tries to reduce the most relevant components of the uncertainty in the world model, for the task the robot is currently performing. It is task oriented in the sense that it explicitly considers a task-specific value function. As test-bed for the presented active vision approach, we selected ...

This paper presents a convergent scheme for Hamilton-Jacobi (HJ) equations posed on a junction. The general aim of the approach is to develop a framework using similar tools to the variational principle in traffic theory to model intersections taking in account many incoming and outgoing roads. Then a time-explicit numerical scheme is proposed. It is based on the very classical Godunov scheme. ...

We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming for this problem and derive, for the case of a controlled SDE, the corresponding dynamic programming equation in the sense of viscos...

In this paper we want to investigate the following problem: For a given upper bound for the ruin probability, maximize the expected discounted consumption of an investor in finite time. The endowment of the agent is modeled by Brownian motion with positive drift. We give an iterative algorithm for the solution of the problem, where in each step an unconstraint, but penalized, problem is solved....

We consider a two-player, zero-sum diierential game governed by an abstract nonlinear diierential equation of accretive type in an innnite dimensional space. We prove that the value function of the game is the unique viscosity solution of the corresponding Hamilton-Jacobi-Isaacs equation in the sense of Crandall-Lions 12]. We also discuss some properties of this notion of solution.

This paper is a survey of the Hamilton-Jacobi partial differential equation. We begin with its origins in Hamilton’s formulation of classical mechanics. Next, we show how the equation can fail to have a proper solution. Setting this issue aside temporarily, we move to a problem of optimal control to show another area in which the equation arises naturally. In the final section, we present some ...

This paper provides a characterization of viability kernels and capture basins of a target viable in a constrained subset as a unique closed subset between the target and the constrained subset satisfying tangential conditions or, by duality, normal conditions. It is based on a method devised by Hélène Frankowska for characterizing the value function of an optimal control problem as generalized...

We consider several one-period reinsurance models and derive a rule which minimizes the ruin probability of the cedent for a fixed reinsurance risk premium. The premium is calculated according to the economic principle, generalized zero-utility principle, Esscher principle or mean-variance principles. It turns out that a truncated stop loss is an optimal treaty in the class of all reinsurance c...

In this paper we study both the value function and Q-function formulation of the Linear Programming (LP) approach to ADP. The approach selects from a restricted function space to fit an approximate solution to the true optimal Value function and Q-function. Working in the discrete-time, continuous-space setting, we extend and prove guarantees for the fitting error and online performance of the ...