Multiscale optimal control and stochastic problems (Reference: ESR15) ***Provided positions***

• Title : Multiscale optimal control and stochastic problems
  
• Location: University of Padova, Italy
• Advisor: Martino Bardi
• Secondment: INRIA in collaboration with University of Tours, France
• Funding: 36 months
• Contacts:Fabio Ancona; Martino Bardi
  
• Reference: ESR15
• Application deadline: August 31, 2011 or until the position is filled
• Key Words: Perturbed systems, homogenization, HJB equations
• Description of the subject:

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.

The 6 months secondment will be hosted by INRIA, France, in collaboration with Université François-Rabelais, Tours.

• Requirements:  MSc degree in mathematics or a related subject
  

Applications including a full curriculum vitae, and the names and addresses of at least two referees should be sent to Contacts.