Automatica, April 2002, Volume 38, No. 4

Editorial

  By J-P. Martin. Courtesy Collège de France

Jacques Louis Lions

Jacques Louis Lions was born on May, 3, 1928, in the city of Grasse, in southern France. He died on May, 17, 2001 in Paris. He was buried in Grasse, his all time home town. 

To the scientific world, Jacques Louis Lions will be remembered as a mathematician of exceptional gift, the father of the variational theory of partial differential equations having made profound contributions to the whole theory of PDE's, from the most theoretical concerns of definition of solution, existence, uniqueness - let us mention his work on interpolation of Hilbert spaces - to the most practical questions of numerical analysis, his interests embracing also computer architecture and parallelism to implement these algorithms. He authored or co-authored at least 20 books, and nearly 600 articles. Representative of the breadth of his contributions are the very theoretical three volume book with Enrico Magenes on nonhomogeneous boundary problems (1968), and the very applied nine volume series he edited with Robert Dautray on "Analyse mathématique et calcul numérique pour les sciences et les techniques'' (1988). He was Secretary (1978-1991) and then President (1991-1994) of the International Mathematical Union. His scientific work earned him numerous prizes, including the John Von Neumann prize in 1986 and the Japan prize in 1991. 

To the official administrative world, he will be remembered as the founder of the Institut National de Recherche en Informatique et en Automatique INRIA [2] born from IRIA in 1980, and that he shaped for the next 20 years although he remained its President for only four years (1980--1984), the President of the CNES French space agency (1984-1992), the President of countless scientific bodies, including the French Académie des Sciences (1997-1999) and the scientific board of the Office National de la Météorologie, and the inspirer of many more initiatives. He was made Commandeur de la Légion d'Honneur, an extremely high distinction. 

But to his co-workers and friends, he will be much more remembered as a man of great vision and wisdom, always available when you would need his advice, with a solid sense of humour even in serious situations and a great care for individuals. He was such a nice personality that his charm would operate on everybody around him, from clerks to angered union leaders, who would feel that they had really been listened to and taken seriously. This man, who accomplished more in any time span than several of us together, never seemed to be in a hurry.

One should also notice his keen interest for international cooperations with less developed countries. He is also quoted as the first French mathematician (together with Laurent Schwartz) to get in touch with the Italian mathematical community after World War 2, a typical instance, together with his very strong involvement in the Global Change program including its political aspects, of his active, though always modest, concern for peace and friendship in this world.

 

Jacques Louis Lions' interest in control theory grew to a large extent from his contacts with Pierre Faurre and Alain Bensoussan, two classmates of École Polytechnique, who both played an important role in the LABORIA laboratory of IRIA and the birth of INRIA. Alain Bensoussan was to become Jacques Louis Lions' successor at the chairmanship of both INRIA and CNES [3] with a three year gap at CNES). Pierre Faurre headed for an industrial career as the chairman of the board of SAGEM, before he died prematurely a few months before Jacques Louis Lions.

Pierre Faurre had obtained a PhD at Stanford University with R.E. Kalman in 1967. He is said to be the one who drew Jacques Louis Lions' attention to system theory and control. This must have happened very early and quickly, since as early as 1966, Jacques Louis Lions gave a thesis topic to Alain Bensoussan which, in modern words, was the adaptive control of infinite dimensional systems. A. Bensoussan was to develop first the filtering theory, and this was the topic of his Doctorat d'État (and the first "cahier du Laboria") in 1969 (and a book in 1971). In between, Jacques Louis Lions had published his first major work on control theory, still often quoted : "Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles'' (1968). 

The collaboration between Jacques Louis Lions and Alain Bensoussan went on with their work on stopping time control and variational inequalities and later on impulse control and quasi-variational inequalities, a concept they introduced specifically (in 1973) for its control application. This gave rise to a series of joint papers and books starting in 1973. 

Of particular relevance to automatic control was also Jacques Louis Lions' work on exact controllability of PDE's, his "HUM" (Hilbert Uniqueness Method) which was the topic of his 1986 John Von Neumann lecture and of a book in 1988, his theory of "sentinels" for the detection of events difficult to monitor directly (this was in connection with his work on environmental issues), singular perturbation of boundary geometry (for the study of the effect of ailerons in aircrafts), and so many other ideas that we cannot quote exhaustively. At least nine of his published monographs are about control theory.

 

The extent and depth of Jacques Louis Lions' scientific contributions do not suffice by themselves to completely explain his immense influence on French, and in a large extent World, applied mathematics. 

We have said that Jacques Louis Lions was a man of vision. In the 50s and 60s, the French mathematics were entirely dominated by the Bourbaki school. Getting interested in practical solutions of physical problems, and worse, in numerical computation, was a lonely and seemingly hopeless attempt, and looked as a dead end. Yet, he was to bring Systems Analysis and Control to the Collége de France, the highest institution in the French academic system, where he was a professor from 1973 to his retirement in 1998. This is a tribute to his unique capacity to foresee what would become important problems, and inventing powerful ways of looking at them from a mathematical viewpoint. Then he would most often hand out the topic to a student, and let him go forth seemingly on his own ideas, although he would always be available to talk with him. Some recall that he would claim he was learning from his students - to their greatest amazement - and he had so many (probably over 50) that he must have learned a lot. This generous attitude, together with his unsusual mathematical gifts, made him, in effect, the father of a whole school of French applied mathematicians, of which the sixth generation is now being born. 

No doubt that the achievements of his scientific heirs were his second most important claim of proud. The first one was his son's Pierre-Louis' own achievements, that earned him a Field medal in 1994.

 

Seldom has a single man displayed so many abilities and gifts, seldom will a scientist be so much missed by his colleagues and friends.

Pierre Bernhard

This paper is very much based upon memoriam papers by Roger Temam and Jean-Pierre Aubin. The author also thanks Jean Céa and Alain Bensoussan for their help.

Notes

[1]  National Institute for Computer Science and Control.

[2]  One day when the young INRIA was sailing through unusually rough waters, he sent his coworkers one of his usual handwritten notes that read "1) Keep calm, 2) keep desperately calm, 3) ...''.

[3] He is now also chairman of the European Space Agency.