The legacy of Jan Willems

On 31 August, Jan Willems, Emeritus Professor of Systems and Control Theory, passed away. Willems was a world-renowned pioneer in Systems and Control, and the founder of what is now the Systems, Control and Applied Analysis Group at the Johann Bernoulli Institute for Mathematics and Computer Science.

The field in which Jan Willems worked was a broad one. Systems and Control theory may sound a bit dull, but it is important for the thermostat in your home, your car’s suspension and the positioning of the GPS satellite network that makes Sat Nav possible.

‘Jan Willems belonged to the second generation of pioneers in this field’, says Professor Harry Trentelman, himself a former graduate and PhD student under Willems. The first generation, the founding fathers of the field, dated back to the 1930s. ‘When the telephone system expanded, engineers struggled with the question of how to boost the signal over telephone cables that ran from California to New York.’

This problem was tackled in the famous Bell Labs . ‘They had to make amplifiers that boosted the signal, even though that could have rendered the signal unstable. Therefore, they needed amplifiers with feedback.’ Such a system, with input and output, is at the heart of all Systems and Control science. ‘Basically, we wanted to include the system in a mathematical model, to understand how it could be controlled.’

At the end of the 1950s the well-known Sputnik Shock further boosted the development of Systems and Control, through the United States space programme. This programme included the mathematical theory of analyzing the dynamics of spacecraft and the estimation of variables in the presence of noise. The famous Kalman Filter was developed to deal with this problem.

Willems, who was born in Bruges in Belgium, trained as an electrical engineer at the University of Rhode Island in the United States and gained a PhD in Electrical Engineering from the Massachusetts Institute of Technology (MIT) in 1968. His thesis discussed feedback systems. After several more years as Assistant Professor at MIT, he was appointed a full professor at the University of Groningen.

‘His background as an electrical engineer meant he was firmly rooted in the physics of the systems he was working with, although his main interest lay in the fundamental, theoretical part of a problem’, explains Trentelman. ‘Despite the fact that he wasn’t a recognized mathematician, he knew his maths better than most.’

This combination of a practical background, mathematical skills and a yearning for deep theoretical knowledge made Willems one of the world leaders in Systems and Control Theory. ‘He formulated several founding principles, through which he connected different problems in one theoretical framework.’

His work resulted in a number of important prizes, such as the IEEE Control Systems Award in 1998, but also numerous chair positions at major conferences, editorships of journals and so on. In the Netherlands he put the University of Groningen on the map in Systems and Control Theory, and he was instrumental in creating the Dutch Institute of Systems and Control (DISC), a national graduate school and research network.

‘Willems also created his own school’, says Trentelman. ‘Like me, there are now some 10 full professors who studied with him in the 1970s and 80s, so Willems has a lot of scientific “children” and even “grandchildren”.’ Trentelman worked closely with Willems until his retirement in 2003. ‘After retiring, though, he continued working and produced around 100 papers in the last 10 years!’

Only in recent years did he slow down due to a serious illness. ‘It was such a pity, as there was so much he still wanted to do. At the end of his career he was more and more focused on the fundamental questions in his field.’

‘We met a few times each year, in Groningen or at some international conference’, Trentelman says. ‘He was always good company and he had what is nowadays called the “X-factor”. He could really get things done.’

The legacy of Willems at the University of Groningen is the focus on the theory of Systems and Control. Apart from the group of Trentelman and his colleagues, there’s ITEM, the Institute for Technology, Engineering and Management. ‘Willems really was one of the great scientists of this Faculty. His citation ranking is higher than almost any other Faculty member in mathematics.’

Willems’ successors have successfully built on this foundation. Next year the biannual conference on Mathematical Theory of Networks and Systems will be held in Groningen. ‘That is a sign that we’re still doing well.’ During this conference, in July 2014, a special memorial session is planned to discuss the work and legacy of Willems. ‘There will be lectures on his work, but also plenty of anecdotes and humour. That was typical of Jan.’

Harry Trentelman has written an In Memoriam for Jan Willems (1939-2013)