PhD Position F/M Modeling and Control of Large-Scale Density Systems via the continuation process

Inria
November 17, 2022
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2022-05456 - PhD Position F/M Modeling and Control of Large-Scale Density Systems via the continuation process

Contract type : Fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position

About the research centre or Inria department

Le centre de recherche Inria Grenoble - Rhône-Alpes regroupe un peu moins de 600 personnes réparties au sein de 22 équipes de recherche et 7 services support à la recherche.

Son effectif est distribué sur 3 campus à Grenoble, en lien étroit avec les laboratoires et les établissements de recherche et d'enseignement supérieur (Université Grenoble Alpes, CNRS, CEA, INRAE, …), mais aussi avec les acteurs économiques du territoire.

Présent dans les domaines du calcul et grands systèmes distribués, logiciels sûrs et systèmes embarqués, la modélisation de l'environnement à différentes échelles et la science des données et intelligence artificielle, Inria Grenoble - Rhône-Alpes participe au meilleur niveau à la vie scientifique internationale par les résultats obtenus et les collaborations tant en Europe que dans le reste du monde.

Context

Scientific Context

Current research in control theory is aiming to harness the dynamics of large networks, such infrastructure (traffic, transportation, multi-agent systems, epidemic spreading, electrification of vehicles, etc.). Faced with large number of state variables describing the nodes or the edges and with large uncertainties, there is need for new reduction methods that are appropriate for networks and can navigate through scales.

Assignment

Work program.

The project objectives are: to address several open theoretical problems relative to the continuation method and, apply our results to the electro mobility domain.

Supervisor : Carlos Canudas-de-Wit (DR-CNRS)

Application type: PhD. Gross salary: 2 135 Euros/M (CNRS PhD official salaries).

Start: any time after January 2023 Duration : 36 months.

Employer : CNRS. Location : Grenoble, France (GIPSA-Lab and INRIA- RA)

Applications: send motivation letter and CV to carlos.canudas-de- wit@cnrs.fr

Request Background. Control Systems, Applied mathematics

Main activities
  • Accuracy, Convergence & Reversibility. The problem here is to understand to which extend, the PDE approximation can capture all the effects of the original ODE, and how the order of continuation (the highest spatial derivative) affect the accuracy and convergence toward the original ODE solutions.
  • Density-based models . Usually PDEs have derivatives written with respect to the time and space variables. However, it is possible to writing a PDE with derivatives with respect to some other variables. PDEs with “index derivatives” are very useful in moving multi-agent setups, when states of the agents are represented by their positions (called here density-based models, see 5). We propose to study the dependence of the quality of the obtained model on the chosen position function and to provide some justified guidelines on how to make this choice.
  • Density-based models with multi-modal attributes . Another problem of interest concerns a new class of systems that, in addition to the moving spatial agents' variables, have also additional multi-modal attributes. For example, electrical vehicles in electro mobility networks, are not only characterized by their positions and velocities, but also by additional variables modelling the carried/used energy in the vehicle batteries.
  • Local for Global behavior. Another problem to be investigated is how the local interactions affect the global behaviors of the PDE approximation. By local interaction, we mean the characteristics of the local connections in terms of parameters and connectivity. In this project we wish to investigate, at a general theoretical level, how the generic properties of the ODE network (values, connection parameters, graph structure, etc.) affect the global properties of the PDE.
  • Multi-modality controlled proxies. The advantage of the continuation method is that it allows recovering a PDE which describes the same physical system as the original ODE network. Such a description can be very helpful not only for analysis, but also for control purposes. Indeed, one can use an obtained PDE to design a continuous control which, being discretized back, results in a control law for the original ODE system. In the project, we wish to study other possible forms for the control proxis adaptable for other systems including the multi-commodity where in addition to the density-like properties (particle motions); they possess additional attributes (i.e. energy carried by the particles). Control proxis with multi-commodity will imply to target PDEs proxis with high- dimensions, and in turn, this will imply for continuation approximation to look for high orders differentials. We will then investigate questions about existence of the approximations and the associated construction methodology to design the control law.
  • Study-case: Electro-mobility. The integration of the electrical vehicles (EV) with the city infrastructure (charging stations), and the electrical power supply network possess unsolved critical problems that will become critical with the massive adoption of EV by the population. In the current literature, models capturing the EV mobility and energy stored in the vehicles do not exist. Those models are necessary premises to start to understand how to optimally balance demand/supply energy between the VE (demand) and the power (supply) networks. Models that combine EV motions models together with the energy consumed and carried by the vehicle will be devised by using the continuation models with multi-modality. Besides, problems of evaluating, locating, and designing charging stations to support the VE power demand will be also addressed. In the PDE continuation model, the charging stations are point sources that also need to be considered. Electrical vehicles can also be seen as a storage energy elements feeding energy back to the power network to balance the power demand.
  • Benefits package
  • 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
  • General Information
  • Theme/Domain : Networks and Telecommunications System & Networks (BAP E)

  • Town/city : Montbonnot

  • Inria Center : CRI Grenoble - Rhône-Alpes
  • Starting date : 2023-01-01
  • Duration of contract : 3 years
  • Deadline to apply : 2022-11-17
  • Contacts
  • Inria Team : DANCE
  • PhD Supervisor : Canudas-de-wit Carlos / carlos.canudas-de-wit@inria.fr
  • The keys to success

    Automatic - applied math

    About Inria

    Inria is the French national research institute dedicated to digital science and technology. It employs 2,600 people. Its 200 agile project teams, generally run jointly with academic partners, include more than 3,500 scientists and engineers working to meet the challenges of digital technology, often at the interface with other disciplines. The Institute also employs numerous talents in over forty different professions. 900 research support staff contribute to the preparation and development of scientific and entrepreneurial projects that have a worldwide impact.

    Instruction to apply

    Defence Security : This position is likely to be situated in a restricted area (ZRR), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST).Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision, as defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result in the cancellation of the appointment.

    Recruitment Policy : As part of its diversity policy, all Inria positions are accessible to people with disabilities.

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