Averaging and ergodic optimal control problems (Reference: ESR12) ***This position has been filled***

• Location: Université Pierre et Marie Curie  and   Université de Bretagne Occidentale (UBO)
• Secondment: Università degli Studi di Padova (USP)
• Application deadline: February 28, 2011
• Advisor: Helene Frankowska and   Marc Quincampoix 
• Contact:  Helene Frankowska

The ergodic control problem, namely the asymptotic behaviour of the value of an optimal control problem when the horizon converges to infinity, is classically studied through a limit of a suitable Hamilton-Jacobi-Bellman equations.  In terms of the control system this requires controllability and dissipativity assumptions. The goal is to weaken this controllability assumption and to investigate the nonconvex Hamiltonian case (differential games) which still remains widely open. This is a research area, having connections to averaging methods for singular perturbations systems, which remains largely unexplored.

Applicants are expected to have a degree in Mathematics or Applied Mathematics and a good knowledge of optimization or control theories.