Dante Kalise

Dante Kalise - University of Rome

• Main host organisation: Università Degli Studi di Roma - La Sapienza, Italy
• Supervisor: Maurizio Falcone
• Secondment organisation: Universität Bayreuth, Germany
• Fellowship duration: November 2011 - April 2013
• Email address

• Background: Dante holds a PhD in Applied Mathematics from the University of Bergen, Norway. His research is related to the construction and analysis of numerical schemes for the solution of partial differential equations; more specifically, he works on high-order methods for the solution of hyperbolic problems and its applications to optimal control and differential games.  Other areas of interest are: atmospheric modeling, data assimilation and algorithms for dimensional reduction.

SADCO Project title: Numerical Methods for Differential Games

The approximation of the value function for differential games is a difficult task due to the presence of  discontinuities in the solution. In fact, even for rather simple classical problems such as the homicidal chauffeur the value function has jump discontinuities. Although the schemes derived by dynamic programming techniques have shown to be effective, a complete and satisfactory convergence theory is still missing for the discontinuous case. The aim of this project area is to provide such a convergence theory. We shall also examine procedures for the approximate synthesis of the feedback control via the value function. Here, new theory is required to show that the approximate optimal trajectories obtained by numerical synthesis converge to the true optimal trajectories, in the limit as the discretization parameters tend to zero.

SADCO related publications