2020-02818 - PhD Position F/M PhD position on Adaptative observers for propagative systems and associated discretization: formulation and analysis
Le descriptif de l’offre ci-dessous est en Anglais

Type de contrat : CDD

Niveau de diplôme exigé : Bac + 5 ou équivalent

Fonction : Doctorant

Niveau d'expérience souhaité : Jeune diplômé

A propos du centre ou de la direction fonctionnelle

Located at the heart of the main national research and higher education cluster, member of the Université Paris Saclay, a major actor in the French Investments for the Future Programme (Idex, LabEx, IRT, Equipex) and partner of the main establishments present on the plateau, the centre is particularly active in three major areas: data and knowledge; safety, security and reliability; modelling, simulation and optimisation (with priority given to energy).   

The 450 researchers and engineers from Inria and its partners who work in the research centre's 28 teams, the 60 research support staff members, the high-level equipment at their disposal (image walls, high-performance computing clusters, sensor networks), and the privileged relationships with prestigious industrial partners, all make Inria Saclay Île-de-France a key research centre in the local landscape and one that is oriented towards Europe and the world.

Contexte et atouts du poste

The thesis will be supervised within the team M$\sf{\Xi}$DISIM (joint team between Inria and Ecole Polytechnique) by P. Moireau expert in observer theory for infinite dimensional systems. It will be done in collaboration with S. Imperiale, (LMS, Inria Saclay, M$\sf{\Xi}$DISIM) whose area of expertise is wave propagation, numerical analysis and inverse problems.

Finally, this PhD Thesis is part of the ANR ODISSE (https://anr-odisse.univ-lyon1.fr/index.html), hence the candidate will have to closely interact with colleagues in this thesis, in particular K. Ramdani, J. Valein and J.C. Vivalda from Inria Nancy-Grand Est, Team Sphinx, but also with M. Boulakia and M. De Buhan collaborators in the ANR.

Mission confiée

In this thesis we plan to study observer methods for propagative systems, from wave equations, transport equations but ultimately more general propagative systems. Our question is to design analyze, discretize, and perform the numerical analysis of such methods. But more importantly our goal is to use observer methods to propose efficient parameter identification methodologies.

Asymptotic reconstruction of unknown constant parameters in finite-dimensional dynamical systems is a very well-studied problem. Many algorithms that have been developed link persistence of excitation notions of some input variables with the asymptotic estimation (namely observer) problem. Analyzing these techniques to hyperbolic PDEs is a promising approach. In particular, we plan to investigate the problem of source identification using adaptive observers where we link Carleman estimates on Hyperbolic PDEs with observer design strategies.

Then, we plan to develop a reconstruction strategy for more general parameter dependencies based on iterative reconstruction strategy of source problems. Indeed, we expect in the case of perturbed parameters to justify by asymptotic analysis a model reduction that changes the problem of parameters recovery to a problem of source recovery, since the parameter influence enter the asymptotic expansion of degree n only combined with the expansions of inferior degrees. The full convergence of the iterative process can then be studied by combining the observability condition obtained on each expansion and stability result on the iteration from expansion to the next with similar mechanisms as in reconstruction strategies based upon iterated Born approximations. Such approach could pave the way of a systematic strategy for the identification of PDE with linear-dependent parameter multiplying the solution.

Principales activités

 

Examples of tasks:

  • Adaptive observer design
  • Numerical methods for observer
  • Numerical analysis of the resulting observers
  • Application to propagative systems, in particular wave propagation in the heart

Compétences

Skills in control theory and programming are definitely a plus.  

Avantages

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage

Rémunération

Monthly gross salary  (1st and 2nd year) : 1.982 euros

Monthly gross salary (3rd year) : 2.085 euros