Publications SCIENTIFIC WORKS

In 1990, I defended my PhD thesis at the LIX laboratory. My thesis advisor was Marc Giusti with whom I began to work in 1986 at the Centre de Mathématiques (now Laurent Schwartz laboratory). My subject was to design identifiability test by using computer algebra to solve polynomial equations. I discovered in 1988 differential algebra in the work of Wu Wentsün who gave a lecture at Institut Henri Poincaré in Paris. At that time, the use of differential algebra in control was already introduced by Michel Fliess, with whom I met at that time.

In the nineties, my team went back to the Centre de Mathématique, created the GAGE laboratory, and then UMS MEDICIS providing computer services to the computer algebra community. Those years were devoted to a long term work on differential flatness, a notion characterizing differential systems whose solutions may be parameterized by m arbitrary functions. This non generic property is very common in the engineering practice. It allows solving easily motion planning problems and already has many practical applications in the industry. It is also related to many unsolved mathematical problems.

I also worked in differential algebra, mostly on some algorithmic aspects. I was the thesis advisor of Ariane Péladan-Germa, who developed a method for testing zero equivalence in differential rings extensions. I was also coadvisor of Brahim Sadik’s thesis Abdelilah Kandri-Rody of Marrakech University and we are still working together since that time.

With Marc Giusti, I was coadvisor of Alexandre Sedoglavic’s thesis. This work made a link between some aspects of the formal resolution of algebraic andd differential algebraic systems and motion planning for some systems described by non linear partial differential equations characterized by a property analogous to flatness. Here are some animations illustrating his results: A non linear wire A non linear flexible rod.

Alexandre Sedoglavic also developed a very efficient algorithm to test local identifiability, and implemented it in Maple.

With the new century, after the sudden suppression of UMS MEDICIS, we went to the newly created STIC department of CNRS and created FRE STIX with a more applicative and pluridisciplinary activity. Some research contracts have compensated the decrease of basic research financial support. We are working with CNES, ONERA and APPEDGE on the CARINS project, devoted to the simulation of liquid propellants rocket’s engines. We also work with APPEDGE around the DIFFEDGE software for automatic differentiation of function defined by block-schemes in Matlab-Simulink which offers many opportunities to illustrate and develop new advances made in our team in linear control.

The identifiability theme also led me to invest, under the influence of Daniel Claude, in research projects mixing control theory and biology, such ACI SCARAMOCO.

Working group modeling and control of biological systems.

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