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Early stage researcher (PhD student) – Multiscale optimal control and stochastic problems

Deadline august 31, 2011 or until the position is filled

ARGOMENTI: Valutazioni comparative

A PhD position is available within SADCO Initial Training Network, funded by the Marie Curie actions under the FP7 People programme from the European Commission at the University of Padova. The network offers unique cooperation possibilities in control theory, allowing each recruited researcher to carry out a part of his/her project at another institution during his/her tenure within the network.
The appointment will be for 3 years, and the successful applicant is expected to register for a PhD programme at the Department of Pure and Applied Mathematics at the University of Padova, which offers a very good environment in Control and PDE's (see website:
http://www.math.unipd.it/?l1=ricerca&id_ricercaarea=7). He/She will carry out his PhD Thesis under the supervision of Prof. Martino Bardi. The PhD position entails a six-month secondment hosted by INRIA, France, in collaboration with Université François-Rabelais, Tours.

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.

Salary

The salary and terms of employment will follow the Marie Curie rules of the European Commission (40k Eur/year before taxes, plus mobility allowance, and travel and career exploratory allowances). Substantial funding for participation in conferences and other research and training activities will be also offered.

Qualifications:

-University education in mathematical analysis
-Knowledge of oral and written English
-Ability to collaborate in a network
-Experience in research collaborations

Eligibility

The candidate can be of any nationality (European or non European), but he/she will not have resided or worked in Italy for more than 12 months in the 3 years prior to the recruitment. The researcher must also be in the first four years (full-time equivalent) of his/her research careers.
Applications including a full curriculum vitae, and the names and addresses of at least two referees should be sent to :
bardi@ math.unipd.it
and
ancona@math.unipd.it
Subject: Application for PhD position (ESR15) )

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