23/03/2021
The Human Resources Strategy for Researchers

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

This job offer has expired


  • ORGANISATION/COMPANY
    INSA Rouen Normandie
  • RESEARCH FIELD
    Information science
    Mathematics
  • RESEARCHER PROFILE
    First Stage Researcher (R1)
  • APPLICATION DEADLINE
    20/06/2021 12:00 - Europe/Brussels
  • LOCATION
    France › SAINT ETIENNE DU ROUVRAY
  • TYPE OF CONTRACT
    Temporary
  • JOB STATUS
    Full-time
  • HOURS PER WEEK
    35
  • OFFER STARTING DATE
    01/09/2021
  • REFERENCE NUMBER
    DOCTORANT LMI

OFFER DESCRIPTION

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.

 

More Information

Eligibility criteria

The application requirement is a Master degree with strong background in applied mathematics, in

particular in probability theory and/or in analysis of PDEs.

Some knowledge in control theory and/or Optimization and/or numerical analysis will be appreciated.

Some knowledge of programming skills (C++, matlab, python etc) is required.

Good written and oral English language skills are required.

Personal characteristics:

- Motivation for conducting research at an advanced level

- Good communication skills

- Ability to work independently and in a team

The application should be accompanied by a detailed CV, a motivation letter, and the name of two referees

(to whom a recommendation letter will be requested, if the candidate is shortlisted).

Applications will be reviewed as they are received until June 1st, or until a suitable candidate is found.

Offer Requirements

  • REQUIRED EDUCATION LEVEL
    Mathematics: Master Degree or equivalent
    Information science: Master Degree or equivalent

Skills/Qualifications

The subject of this thesis concerns the development of new theoretical and numerical

approaches for some control problems governed by partial differential equations.

Control theory of SPDEs have already been studied in many contributions. Several results have been

established regarding the exact, null or approximate controllability properties for various stochastic

equations (of transport, parabolic or hyperbolic type). An extensive literature have been also devoted

to the stability analysis of SPDEs providing valuable insights into the regularity and global behaviour

of the solutions of SPDEs.

Besides, new mathematical tools have been introduced to extend the theory of optimal control

problems governed by SPDEs. Necessary or sufficient optimality conditions have been derived for a

class of control problems, providing important information on the nature of optimal controls, in particular,

for situations in which optimal controls can be realised by a feedback control law.

Many practical optimal control problems involve constraints on state variables, to avoid some

regions of the state space where perhaps operation is unsafe or the dynamic models considered are no

longer valid. The current contributions on control of SPDEs do not take account of such constraints.

The understanding of state-constrained optimal controls is in many important respects incomplete, and

important questions concerning the structure of optimal state constrained trajectories, higher order

conditions, conditions for local optimality and efficient computational methods are still open.

The aim of this project is to further develop the fundamental theory of optimal control problems

of SPDEs under end-point or/and distributed state constraints, and also to provide computational

schemes for their solutions.

Specific Requirements

The application requirement is a Master degree with strong background in applied mathematics, in

particular in probability theory and/or in analysis of PDEs.

Some knowledge in control theory and/or Optimization and/or numerical analysis will be appreciated.

Some knowledge of programming skills (C++, matlab, python etc) is required.

Good written and oral English language skills are required.

Personal characteristics:

- Motivation for conducting research at an advanced level

- Good communication skills

- Ability to work independently and in a team

The application should be accompanied by a detailed CV, a motivation letter, and the name of two referees

(to whom a recommendation letter will be requested, if the candidate is shortlisted).

Applications will be reviewed as they are received until June 1st, or until a suitable candidate is found.

Work location(s)
1 position(s) available at
INSA ROUEN NORMANDIE
France
SAINT ETIENNE DU ROUVRAY
76801
Avenue de l université

EURAXESS offer ID: 618995

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