PhD thesis proposal in applied mathematics “Optimal Control Problems governed by Stochastic Partial...
INSA Rouen Normandie
State University, Browse similar opportunities
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State University, Browse similar opportunities
Advisors: Hasnaa Zidani & Nicolas Forcadel
Location: LMI - Laboratoire de Mathématiques de l’INSA Rouen Normandie, France
Contact: hasnaa.Zidani@insa-rouen.fr
Doctorale School: MIIS - Mathématiques, Information, Ingénierie des Systèmes (Normandie)
Fellowship duration: 36 months
The PhD candidate will be part of the group “Optimization, Control” in the Applied Mathematics
Laboratory - LMI - at INSA Rouen Normandie.
The laboratory provides a rich and stimulating environment for demanding and high-level research
in applied mathematics combining theoretical subjects and challenging applications. In
particular, the PhD thesis is part of a research project “Chaire d’Excellence - COPTI”, lead by
Prof. Hasnaa Zidani, and funded by Région Normandie.
The gross salary is about (~1800 euros per month), the PhD student have also the possibility
to apply for a teaching position (raising the salary).
For international applicants: Euraxess Normandie provides support for the administrative processes
(further information available on the website: https://www.normandie-univ.fr/international-
2/euraxess-en-normandie/euraxess-in-normandy/).
Optimal control concerns the determination of control strategies for complex systems, with the
aim of optimising their performances and making them evolve according to well-defined objectives
(reaching a target, avoiding obstacles or observers, etc). This field of research was born in the 60s,
motivated by the “space race” and the need to develop a new theory and new computational methods
for the determination of flight paths in space exploration. The field now has a much broader scope
than what early applications to aerospace engineering would suggest, and now encompasses applications
where the state system describe challenging scientific and technological phenomenon with
social, economic and environmental impacts of great importance (in neuroscience, climate modelling,
geophysics, chemistry, financial mathematics, etc.).
The foundations of the field of optimal control theory are now well established and have
benefited from several important contributions developed in recent decades using different mathematical
tools (geometric control, optimisation theory, variational analysis, partial differential equations,
numerical analysis, etc.). However, the new applications coming from more complex technologies require
additional developments, and calling on modern tools, in order to be able to consider concrete
problems involving nonlinear complex systems submitted to uncertainties of the model or the environment.
Stochastic partial differential equations (SPDEs) are the most adequate modern mathematical
tool for modelling many biological, physical and economic systems subjected to the influence of
noise, whether intrinsic (modelling uncertainties, random initial conditions...) or extrinsic (environmental
influences, random forcing, …). In many cases, the presence of noise leads to new physical
behaviours and new mathematical properties. SPDEs have become an important field in mathematics,
at the intersection of probability theory and analysis of partial differential equations. Many significant
advances have been achieved in recent years leading to the development of a rigorous general theory
that provides a precise meaning to the notion of solutions and also an adequate framework for
analysing numerical algorithms devoted to the approximation and computation of these solutions.
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