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Pravin Varaiya is Nortel Networks Distinguished Professor in the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley. From 1975 to 1992 he was also Professor of Economics at Berkeley. During 1994-1997 he was Director of California PATH, a multi-university research program concerned with the development and use of technology to help solve California’s transportation problems. His current research is concerned with sensor networks, transportation, and hybrid systems. His earlier research dealt with stochastic control, communication networks, discrete event and large scale systems. Varaiya has held a Guggenheim Fellowship and a Miller Research Professorship. He has received two Honorary Doctorates, and the Field Medal and Bode Prize of the IEEE Control Systems Society. He is a Fellow of IEEE, a member of the National Academy of Engineering, and a Fellow of the American Academy of Arts and Science. He is on the editorial board of Transportation Research--C. He has co-authored three books and 300 technical papers. The second edition of High-Performance Communication Networks (with Jean Walrand) was published by Morgan-Kaufmann in 2000. “Structure and Interpretation of Signals and Systems” (with Edward Lee) was published in 2003 by Addison-Wesley.
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It is an honor to receive the Bellman Award. I am sure the Award Committee received many outstanding nominations, and I thank the Committee for selecting me. I was invited to make a few remarks, so long as I did not exceed five minutes. I will point out some landmarks along my intellectual journey. The young people among you may find it of some interest. I came to Berkeley as a graduate student in 1960. I owe a great deal to Professor Lotfi Zadeh who was my PhD adviser and who has been a mentor to me ever since. Much of my intellectual development came from interaction with visitors and students. Karl Astrom visited me in the early 1960s. His paper with Bohlin on system identification became for me a standard of research quality and research exposition. Another significant visitor was Bill Root. Bill showed me how to use mathematics in the analysis of communication systems, and he introduced me to information theory.
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There was a buzz at the time about white noise and martingales. Gene Wong was talking about it, as was Moshe Zakai. Tyrone Duncan was visiting. Ty de-mystified the buzz for me. He taught me how to think about stochastic systems. Thus began my lifelong attraction towards randomness. Sanjoy Mitter, who I first met about that time, reinforced that attraction. Sanjoy became a lifelong friend, for which I am very grateful.
Mark Davis was the first in a sequence of brilliant PhD students in stochastic systems. Mark discovered the deep relation between martingales and optimum decisions. Rene Boel, Jan van Schuppen, and Gene Wong found that martingales were also key to point processes as well as Ito processes. Jean Walrand grasped this insight and developed it into an outstanding thesis on queuing networks. Venkat Anantharam knew little or nothing about probability theory when he began his PhD. I still recall how much he impressed me with his spectacular work on multi-armed bandits. The third in this group was Vivek Borkar. Vivek was the most quiet, but equally stunning.
This was when P.R. Kumar visited Berkeley. He is the first of the next generation that I got to know as a friend. I have become a fan of his, along with so many others. Intellectual life moves in circles. Borkar and Kumar re-connected me with Karl Astrom, this time through his paper with Wittenmark.
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Jean Walrand introduced me to computer communication networks. This has continued to be an area of research for the past twenty years. We've had outstanding students, who have gone on to brilliant careers. Sri Kumar, then at Northwestern, Jean Walrand and I got to know each other through our interest in networking.
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I learned power engineering in undergraduate school. But then I lost contact with the field, until years later when Felix Wu joined our faculty. Eyad Abed, Fathi Salem and Shankar Sastry wrote their dissertations on difficult questions in nonlinear systems, inspired by problems of power systems. I lost contact with the field once again, until deregulation became the rage in California. Once again Felix recruited me. Felix Wu, Shmuel Oren of IEOR, Pablo Spiller of the Business School, and I joined forces to save California from the clutches of the utilities. We developed a provably good deregulation strategy. The strategy was not adopted.
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Ahmad Bahai and Andrea Goldsmith sparked my interest in wireless communications. They have become stars. They inspired my very recent students, Mustafa Ergen and Sinem Coleri.
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In the late sixties, Noam Chomsky came to Berkeley and gave a lecture on formal languages. Chomsky's talk opened up a whole world for me. I spent a lot of time learning recursive functions, Turing machines, and Godel's theory. Walt Burkhard wanted to do a thesis on space-time complexity of recursive functions, and he helped consolidate what I had learned. However, my involvement with that subject declined.
My interest was revived by the Wonham-Ramadge paper on discrete-event systems, while Joseph Sifakis, Tom Henzinger and others began the study of time automata. These developments combined to create the area of Hybrid Systems. My students Anuj Puri and Alex Kurzhansky obtained some outstanding results in Hybrid Systems.
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My flirtation with transportation began 30 years ago when I taught urban economics. Mario Ripper was my first doctoral student in transportation planning. My interest then waned. In 1990, Steve Shladover helped spark a national, indeed worldwide, interest in automated highways. Berkeley became a leading research center in highway automation, culminating in a full demonstration in 1997 in San Diego. It was very exciting to work with an interdisciplinary group of experts to build something all the way from theory to demonstration.
Since I could not wait for 25 years before automated highways became practical, my attention shifted to today's highways. My student Karl Petty built the PeMS system, which is now world-renowned as a repository of highway data. Roberto Horowitz and I are now developing a control system for the management of highways. It might become an important follow-on to the PeMS system.
Let me conclude with a remark on Richard Bellman, whom I met in the late sixties. Bellman was a renowned mathematician with contributions in many, many areas. I learned two things from him. First, over the years I continue to marvel at the significance of the optimality principle in the form of the verification theorem, which I have used in many contexts. Second and more important, I learned that good theory is very practical.
Thank you very much for being such courteous listeners.