João Meireles

  João Meireles - University of Padova

• Main host organisation: Università degli Studi di Padova, Italy
  
• Supervisor: Martino Bardi
• Secondment organisation: Inria, in collaboration with the University of Tours, France
• Nationality: Portuguese

• Fellowship duration: February 2012 - December 2014
• Background: João obtained a master's degree from the Instituto Superior Técnico, Portugal in 2012.
• Email address 

SADCO project subject: Multiscale Optimal Control and Stochastic problems

Reducing the dimension of the state space is important for many applications, especially when using the Dynamic Programming approach. A rigorous way to decouple variables evolving on fast time scale (m-dimensions) from slower variables (n-dimensions) is by means of Singular Perturbations (briefly, SP), a classical method in ordinary differential equations. A method based on the Hamilton-Jacobi equations associated to optimal control problems was developed by Alvarez and Bardi. It relies on the theory of viscosity solutions and it consists in first finding a limit (effective) Hamiltonian by solving a PDE problem in R^m (of ergodic type), and then in proving the uniform convergence of solutions of the Hamilton-Jacobi equation in Rn+m to the limit PDE in Rn. If the effective Hamiltonian is associated to a control system, then one gets the convergence of the original value functions to the value function of the limit control problem. The goal of this research is to extend this approach in various directions including differential games and problems with unbounded fast variables.

SADCO related publications