PhD thesis proposal in applied mathematics “Optimal Control Problems governed by Stochastic Partial...
INSA Rouen Normandie

PhD thesis proposal in applied mathematics “Optimal Control Problems governed by Stochastic Partial...

France 20 Jun 2021

ABOUT THE INSTITUTION

INSA Rouen Normandie
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OPPORTUNITY DETAILS

State University
Area
Host Country
Deadline
20 Jun 2021
Study level
Opportunity type
PhD
Specialities
Eligible Countries
This opportunity is destined for all countries
Eligible Region
All Regions

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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