# The European Mathematical Society

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## PhD Thesis proposal in Math & Computer Science

June 24, 2012 - 12:28 — Anonymous
Organization:
University of Franche-Comté, France
Email:
raphael.couturier@univ-fcomte.fr
Job Description:

Title: Semi-decentralized distributed control

Goal: The goal of this PhD is to study the design and the implementation of generic control algorithms for systems composed of distributed MEMS in a semi-centralized context (i.e. only the direct neighbors can communicate).

Experiments will concern the “active skin” developed by the Mechanics department in the context of the Labex project ACTION (see icb.u-bourgogne.fr/labex/index.html). First of all, this platform will be adapted by a student master. Currently, this system performs distributed control close to noise propagating in a nozzle. The control is handled by microphones and speakers disposed along the nozzle boundary. It is computed in real time by a network of independent microcontrollers, each of them being associated with a couple of sensor and actuator. So the challenge is to introduce the possibility of communications between neighbor microcontrollers in order to implement control laws based on communications between neighbors.

The thesis will consist in a theoretical study of distributed control laws suited for the platform and their approximation for an implementation on the microcontrollers network. Three controllers should be established, simulated and then implemented on the platform: two passive ones based on the advection equation and on the square root of the wave equation operator (i.e. the d’Alembertien), and a dynamic one governed by an optimal control law as LQG or H-infinite controls. They will be tested on a simulation that will be built for the occasion. The work will be based on the theoretical frameworks introduced in [1] and [2].

The three steps regarding modeling, control law design and its approximation will have to be optimized as far as computation and communication constraints are concerned. The proposed models and the resulting algorithms should take into account the limited computing capacities of microcontrollers and communications only available between direct neighbors. The key element is certainly the algorithmic complexity in order to be able to obtain a real-time control. In this context, communications play a major role. Finally, taking into account the disturbance of communications and fault of computing units, sensors and actuators will provide more robustness to the system.

Required skills: The candidate must have strong skills in Mathematics especially in Partial Differential Equations and in Computer Science.

Conditions: PhD Thesis at FEMTO-ST. Duration 3 years. Earning: about 1400€/month. Start of the PhD Thesis September 2012. Location: Belfort, France

Application deadline: 9th July. 2012.

Please email a CV and a letter outlining your areas of research interest, along with names and contact details of two referees who can comment on your academic suitability to:
raphael.couturier$univ-fcomte.fr, michel.lenczner$utbm.fr

[1] M. Lenczner, G. Montseny, Y. Yakoubi Diffusive Realizations for Solutions of Some Operator Equations : the One-Dimensional. Math.of Comp. 81(2012), 319-344 .
[2] M. Lenczner, Y. Yakoubi Semi-decentralized Approximation of Optimal Control for Partial Differential Equations in Bounded Domains. Comptes rendus de l'Académie des Sciences - Mécanique, Vol.337, Issue 4, pp.245--250, 2009

Job Categories:
Research institutes
Deadline for Application:
Jul 9 2012
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