Ladies and gentlemen, I am deeply honored to be the recipient of the 2012 IEEE Control Systems Award. It is not easy to express in a few words emotion and gratitude for having been considered for such prestigious Award. Thus, following the tradition, I shall share with you a few personal recollections and experiences.
I graduated in Electrical Engineering in 1965. At that time, the higher-education system in Italy was still very much “old fashioned”. The positive side of this was that we received a deep training in basic sciences, notably mathematics (and this eventually gave me a substantial advantage in my career), while the negative side of this was that there was no such a thing as a PhD program. As a student, I was fascinated by systems and control ideas that were taught by the person who guided my research activity at the very beginning, Antonio Ruberti. These were the times that many people have subsequently dubbed “the times of the big bang”: concepts such as controllability, observability, optimal control, state estimation were driving the evolution of the field and Ruberti’s teaching, in this respect, was timely and captivating.
Intimately related to the concepts of controllability and observability is the concept of minimality and this, in the mid 1960’s, was a rather popular topic. Methods for finding minimal realizations of a transfer function matrix were mushrooming. Extending the concepts of minimal realization to broader classes of systems soon became a challenge for various researchers. Algebra seemed to be the natural tool to address these problems and, with limited use of linear-algebraic tools, I was luck enough to address the problem of finding minimal bilinear realizations in discrete-time. This attracted the attention of Rudy Kalman, who invited me to Gainesville in 1974. It was there that I met Eduardo Sontag and Yutaka Yamamoto, who since then became for me sources of intellectual input.
At the turn of the decade, the geometric approach to analysis and design of multivariable systems, developed by Murray Wonham and Steve Morse, provided a full set of conceptual tools answering the fundamental question “what can be achieved by means of feedback ?”
The 1970’s were the times at which another “bang” occurred: the introduction of differential-geometric methods in the analysis of nonlinear control systems. I like – plagiarizing Cronin – to refer to this decade as to the “green years” of nonlinear control. While the previous decade witnessed enormous progresses in linear system design, the “green years” of nonlinear control witnessed a collective effort of trying to establish an equivalent corpus of theories and results for nonlinear systems. Between 1970 and 1975, a rapid succession of papers broke the ground: Claude Lobry, Henry Hermes, Bob Hermann, Hector Sussmann, Velimir Jurdjevic, Roger Brockett, Art Krener were the leading actors. A new area of research was emerging. These leading actors and a small handful of followers used to meet here and there around the world to compare ideas, almost once per year, at “small Conferences”: in 1972 in Sorrento, in 1973 at the Imperial College (the unforgettable NATO School), in 1974 in Portland, in 1975 in Udine, in 1977 in Taormina, in 1977 on a boat in the Caribbean, in 1978 in Bordeaux, in 1979 at Harvard, in 1980 in Aussois, in 1981 in Bielefeld-Rome.
I must admit that, at the beginning, I barely understood what was going on, because my knowledge of differential geometry was almost nothing. But at the conference in Taormina something happened: Art Krener was presenting the results of his recent work with Bob Hermann, a paper that became – in my opinion – a milestone, a watershed. For me, it was like the “revelation of the truth”, and pushed me to do two things: to learn differential geometry and to invite Krener to Rome for a three-month visit. These were truly lucky times for me: the luck of being in the right place at the right time, the luck of being advised (by Dave Elliott) to learn differential geometry on the book of Bill Boothby and the luck of having the opportunity of sitting next to Art Krener for three months in Rome in the spring of 1979. This was the true turning point in my career: once we had discovered how geometric methods could be used for “feedback design” (since then, all earlier results in nonlinear control had rather been concerned with “analysis”), we rushed to prepare a paper that eventually was brought to the attention of a larger public at the conference in Harvard in June 1979. In 1980, I was invited to give some lectures at the Conference in Aussois, and this gave me the opportunity to write a long tutorial paper that became the germ of a subsequent monograph.
Once the key to access the field of nonlinear feedback design was found, the subsequent decade (the 1980’s) witnessed an explosion of results. One of the most popular was the development of the nonlinear analog of the concept of system’s zeros, jointly pursued with Chris Byrnes. The road to non-linear zeros was initially rough and rocky; two original conference papers had technical mistakes, that eventually had been fixed, but the intuitions were full of consequences and by now the concept is widely appreciated not only in the context of system stabilization but in broader application areas, the most notable of which is that of walking machines, as demonstrated by this year’s Bode lecturer Jessy Grizzle.
The decade of the 1980’s ended with another “revolution”: the introduction of the concept of input-to-state stability, by Eduardo Sontag in 1989. This concept has changed the way in which people address the problem of stabilization of nonlinear systems. It seems fair to say that most of the results that appeared in the 1990’s in the domain of feedback stabilization of nonlinear systems, such as the milestone contributions of Hassan Khalil, Peter Kokotovic, Miroslaw Krstic, Laurent Praly and Andy Teel, owe a lot to Sontag’s ideas.
Illustrious colleagues who, more rightfully than me, have preceded me on this podium, have taken this opportunity to share ideas on the field and experiences on their research career. Some of these experiences are similar to mine. As observed by many, chance is an important factor. When I choose Electrical Engineering, I really wanted to become a practitioner and to work in industry, but then I encountered fabulous teachers who made me loving calculus and what was then called “modern control theory” and this completely shifted my goals. Then, as I said, I happened to find myself at the right time in the right place when nonlinear control theory was about to begin. We should not forget, though, Louis Pasteur’s saying: “chance favors the prepared mind”.
A second important factor is the willingness to constantly seek the simplest and most straightforward conceptual mechanisms leading to the analysis and solution of a given problem. My recommendation, to myself, has always been: don’t be happy right-away with the first argument you see, even if this is correct and complete; try to simplify it as much as possible, and the effort in doing this will eventually pay. This is particularly true in the preparation of tutorial material, were the effort spent inevitably rewards in terms of new ideas and results. Intimately related to this is the willingness to present results in an elegant and understandable-to-all fashion. Some individuals prefer to write papers and books for the colleagues: I rather prefer to belong to the other category of people (and fortunately there are many of such colleagues in our field) who like to write papers and books to be understood by a large audience. If it had not been for such colleagues, I would have continued struggling with technicalities and loosing any underlying basic vision.
A third factor is the focus on far-sighted and fundamental results. Research interests, in our field as in others, are driven by the relevance of emerging applications but also for the irrepressible need of the human mind to understand the fundamentals and to arrive at conceptual synthesis. My recommendation to younger people is to always do so in their research: it is true that we need to appease to our funding agencies (today more than yesterday) buy we should not forget that our ultimate mission is that of expanding the frontiers of knowledge and to do so in such a way that others are able to build-up on the results of our work. Specific research topics may experience ephemeral fortune, jumps will certainly occur, but our underlying basic knowledge will constantly grow.
A question that everybody is supposed to answer at this point is: what will the future of control theory be? My predecessors have expressed opinions that I fully share. Control is a discipline at the crossroads of Mathematics, Physics, Engineering, Computer Science and, now, also Biology. Thus, it is in a privileged position and this won’t change in the foreseeable future. Applications are flourishing, from sustainable development to advanced health-care. There are new conceptual challenges that only from our privileged position can be met. Success stories are in continuous growth, as witnessed by the excellent report prepared by the Control System Society and a growing community responds to the increasing needs with enthusiasm and hard work.
A fourth, indispensible, factor is the help and support, direct or indirect, of other individuals. In my short autobiographic recollection I have acknowledged only those who directly influenced my own work. Crediting all those who influenced my work indirectly would end-up with naming a large part of the Control Systems Society. But my career was also determined by the help by a few other individuals with whom I did not have specific scientific interactions, who nevertheless – generously and unselfishly – promoted me in various forms: John Zaborszky, Manfred Thoma, Hans Knobloch. The help of all of them has been instrumental in bringing my work to the attention of a wider academic community.
And, indeed, this is the time of acknowledging longstanding friendships, such as those of Art Krener and Chris Byrnes, who have always been source of scholarly advice and inspiration, of T.J.Tarn and of a small but exceptional set of former students who have made greener the years of my maturity: Alessandro Astolfi, Lorenzo Marconi, Andrea Serrani, Claudio De Persis. And also the time to acknowledge the unselfish support of outstanding Italian colleagues: Sergio Bittanti, Guido Guardabassi, Edoardo Mosca and Roberto Tempo.
I have mentioned a number of unbelievable fortunate events that happened in my career but I have not yet mentioned the most important of them all: having met, in a sunny afternoon of July 1960 on the shores of the Island of Ischia, Maria Adelaide. This has been the most important event in my life and has determined everything that happened since then, including a comfortable career during which she took enormous care of me and of a growing fabulous family.
Thank you all, again, for your support. To receive this award gives me overwhelming feelings. It is a true, and perhaps undeserved, honor to become part of the community of those who shaped this field.