Current Research

• Interpolation, means, Bregman divergences on the set of semi-definite positive matrices
• Non-linear observers
• Vehicle localisation algorithms

Observers and symmetries?

There are symmetries in the basic laws which govern the physical world. But how can a law be "symmetrical"? According to Feynman we should adopt the definition of Hermann Weyl who says a thing is symmetrical if one can subject it to a certain operation and it appears exactly the same after the operation. So the question is what operation we can do to a an experiment, and leave the result the same. For instance the conservation laws involved in the dynamic models of chemical reactors are independent of the choice of physical units (mol, kg, ...).
What about the estimation algorithms? If an algorithm is meant to estimate a physical quantity why should a certain operation affect the algorithm, and not the physical model? For chemical reactors it seems logical that the estimation algorithms do not depend on the units either. More generally for systems possessing symmetries, the extended Kalman filter (one of the most commonly used nonlinear filter), can change under some operations whereas the system under consideration remains unchanged ! We gave a mathematical framework to model and estimators (observers) possessing symmetries, and re-interpreted the inputs "u" as all the features of the environment having to be moved over such that the model looks the same after the operation. We developped a constructive method to build observers possessing the same symmetries as the physical model.

PhD industrial work with TOTAL

During my PhD with the oil company TOTAL PETROCHEMICALS we studied polymerisation reactors which produce polymers (polyethylene, polypropylene). These reactors are equipped with sensors which measure some physical quantities such as temperature, flows, pressures... Using a simple physical model - as well as the measures - we give, in real time, an estimation of the internal compositions of the reactor (soft sensor). So our objective is to give a quantitative answer to questions such as : how much is there of each reactive and where? What is the quality of the produced polymer? Without having necessarily direct composition measures. The models are based on conservation laws (enthalpy balance, mass balance). In order to derive internal compositions we use estimation techniques of Control (observers, filtering...) et we develop algorithms. These algorithms give a real-time internal image of the reactor and are used for the conduction of the unit. There is no publications relative to this work since it is standard enough and confidential.