Richard E. Bellman Control Heritage Award

It is a great honor to receive the Richard E. Bellman Control Heritage Award. I am delighted to share this recognition with my students, postdocs, collaborators, and colleagues. I thank them and my teachers, mentors, and family for inspiring me, for encouraging me, for their generosity, and for their contagious joy in the exchange of ideas. They have made and continue to make my intellectual and professional journey wonderful and significant.  

I also feel fortunate to have made my intellectual home in the controls field with you as my community. The controls field provides us a robust foundation for the mathematically inclined and intellectually curious, a vibrant community for intellectual exchange and life-long learning, a powerful set of tools for asking new questions and innovating new ways of thinking and doing, and a point of departure for making connections and contributions to fascinating, important and challenging questions in engineering and technology as well as in the natural and social sciences and even in the arts.

As a graduate student I learned control theory and I was exposed to creative research, which gave me the opportunity to develop my own taste for research problems.  I learned how to ask questions that are important and challenging but also tractable.  I learned how to address concrete problems and how to abstract out a general story that could have further impact and connect in new creative ways across disciplines. I learned about the thrill of discovering and making good on the ubiquity and utility of feedback in nature and engineering.  

Almost 25 years ago, as part of a project led by Steve Morse, I started to work on questions on how and why fish move in schools, in collaboration with biologists with expertise in animal behavior. I found it incredibly fascinating, and I remember worrying to Krishnaprasad, my PhD advisor, that I may have made a mistake in not studying ecology and evolutionary biology in graduate school. He very quickly assured me that I could still study these fields, not as a graduate student but as a control theorist and that I was well prepared given how central feedback dynamics are to understanding collective animal behavior.

And I continue to explore and exploit(!) new opportunities that the control field affords through my own work and collaborations and through exposure to the creative work of our community.

There is much that distinguishes our field, but I would point to three important features that make the controls field uniquely relevant and important to the challenges of the day:

1. The ubiquity and utility of feedback. Feedback is everywhere in technology and designed systems. Feedback is also everywhere in our bodies, and across the natural world. Feedback determines stability, adaptability, speed, accuracy, robustness, resilience and more.
2. Control-theoretic abstractions. Our abstractions provide the means to new fundamental understanding and approaches to principled design, the means to generalize from one concrete problem and specialize to another, and the means to translate insights, models, and approaches across seemingly different domains.
3. Tractability and rigor. In control we insist on tractability and rigor because with them we can provide guarantees, we can identify limitations and how much room there is for improvement, and we can make systematic our insights, algorithms and design methodologies.

These three features – ubiquity and utility of feedback, control-theoretic abstractions, and our insistence on tractability and rigor – together make our field relevant to so many others, to fields investigating both technological and natural systems.

They give us the freedom to choose topics and questions that we find fascinating and rich. And they give us opportunity to make contributions, through both theory and application, towards a wide range of challenges. We as a community are already having an impact on addressing a vast array of highly topical problems, including security and safety of technology, robotics and autonomous vehicles, transportation, human-machine interaction, machine learning, energy and the environment, biological systems from cells to populations, biomedical innovations, neuroscience and neuromorphic engineering, social networks and more.

But there is more to do as a community to improve on the relevance and impact of our work.

1. We can and should make our work better accessible to broader audiences. There is significant interest in what we do and a real need for collaborators in other fields to appreciate the value of what we do. But people outside our field often find our papers impenetrable. We need to change that.
2. We can and should embrace the questions our collaborators in other fields are asking and invest in understanding their fields. Collaborations are most successful when everyone learns something new. More than just finding an application for a tool we’ve developed, we can and should dig in and explore how we can make a real difference. It’s amazing how easy it is to get engaged in the questions being asked in other fields. And it means that we aren’t merely bringing our perspective to questions in another field but also bringing something fundamental back to our community.
3. We can and should remain humble. Control theory has much to offer but we need to remember that we have much to learn. Humility is key in making connections across disciplinary divides.
4. We can and should pro-actively promote and welcome a more diverse community. A more diverse community means a richer diversity of expertise, a richer diversity of questions and challenges that drive us, a richer diversity of ways of thinking and approaching research, and a richer diversity of life experience and perspectives.

I am proud to be the second woman to receive this award, and I acknowledge all the women in control who came before me and paved the way for the opportunities that I have had. Thank you to Bozenna Pasik-Duncan, Linda Bushnell, Anu Annaswamy, Dawn Tilbury, and others who have been tireless advocates for women in control.

We have much to do and it is an exciting time for the controls field. I look forward to joining you in next adventures. Thank you very much for this great honor.

Video of Acceptance Speech

Richard Bellman was a paragon of deep foundational thinking and interdisciplinary work, so I am deeply grateful to receive an award that honors him. It is especially meaningful that the prize is awarded by the Automatic Control Council, which brings together such disparate areas of applications in engineering, mathematics, and the sciences.

Exactly 50 years ago, as an undergraduate in Buenos Aires looking for a senior project, I discovered the work of Rudolf Kalman, which sparked a stable and robust attraction to control theory that continues to this day. One of my professors met Kalman at a conference, which led to Kalman inviting me to be his student. Kalman’s rigorous mathematical approach inspired research excellence, deep thinking, and clear exposition. The 1970s witnessed an explosion of new and exciting ideas in systems theory, and many of the leaders in the field visited Kalman's Center. I was extremely lucky to have the opportunity to learn from all of them. 

After my PhD, I went to Rutgers, where I was fortunate to collaborate with Hector Sussmann, and to learn so much from him.

Five years ago, I was recruited by Northeastern University, where I have fantastic colleagues, especially Mario Sznaier and Bahram Shafai.

Of course, I am grateful to all who influenced my work, too many to credit here, and to those who applied, enriched, and extended my initial ideas. At the risk of sounding presumptuous, let me share some thoughts about research in systems and control theory. First, it is important to formulate questions that are mathematically elegant and general. Paradoxically, general facts are often easier to prove than special ones, because they are stripped of irrelevant details. Second, we should strive to simplify arguments to their most elementary form. It is the simplest ideas, those that look obvious in retrospect, that are the most influential, as Bellman’s dynamic programming so beautifully illustrates. Third, we should be aware of the essential connection between theory and applications. Applications provide the inspiration for an eventual conceptual synthesis. Conversely, theory is strengthened and refined by working out particular cases and applications. Fourth, one should be cautiously open to new ideas, even those orthogonal to current fashion. But not all new ideas are good: novelty by itself is not enough. Finally, we should not lose sight of the fact that, while fun and intellectually challenging, our ultimate objective is to improve the world through scientific and engineering advances.

Which brings me back to Richard Bellman’s heritage, which we honor today. Years after his foundational work on optimality, Bellman turned to biology and medicine, even starting a mathematical biology journal. I am sure that the mechanistic understanding of behavior at all scales, from cells to organisms will lead to control and elimination of disease and the extension of healthy lifespans. I find immunology and its connections to infectious diseases and cancer to be a fascinating field for systems thinking. In addition, the associated engineering field of synthetic biology will lead to new therapeutic approaches as well as scientific understanding, and new mathematics and control problems suggest themselves all the time. In my view, the main value of systems and control to molecular biology will not be in applying deep theoretical results. Instead, conceptual ideas like controls, measurements, robustness, optimization, and estimation are where the main impact of our field will be felt.

Thank you so much.

June 9, 2022

Atlanta, GA USA

ACC 2022

To receive the Richard E. Bellman Control Heritage Award is truly an honor. I am thankful first to all of you for attending today after two postponements of these ceremonies due to the pandemic. I am grateful to the honors committee for selecting me, and to my nominator and references for their willingness to put forth and support my nomination.

The Bellman Award is given for “distinguished career contributions to the theory or application of automatic control.” My career in control started as a junior at Swarthmore College in 1972 when I took a course based on the textbook Dynamics of Physical Systems by Robert Cannon. That course really challenged me, and I found myself putting in a lot of time and energy just to get by. That investment sparked my interest, and so as a master's student at Cornell University I worked with Dick Phelan and learned the practical and experimental side of automatic control in the laboratory using analog computers. In 1975 I decided to pursue control engineering for my Ph.D. work and Prof. Phelan said, in mechanical engineering at that time, there were really only two choices: MIT or UC Berkeley. So I wound up at UC Berkeley where I learned controls from Yasundo Takahashi, Masayoshi Tomizuka (Tomi is also a Bellman Award recipient), and Dave Auslander. I not only learned the latest in control theory from the book Control and Dynamic Systems by Takahashi, Rabins and Auslander, but did my first experiments using digital controllers. My doctoral advisor and professional role model, Dan Mote, is a dynamicist, and my research was on reducing sawdust by controlling vibrations of bandsaw blades during cutting and included theory, computation and experiment.

When I started as an Assistant Professor at the University of Michigan in 1980, I had the great fortune to have two very special mentors. The late Elmer Gilbert (another Bellman Award recipient) came to my office to welcome me, to offer his help with the new graduate course I was developing, and to invite me to participate in a College of Engineering control seminar – a regular Friday afternoon seminar which I still continue to attend! The other was my longtime friend and collaborator Yoram Koren, together with whom I conducted many joint research projects, and from whom I learned much of what I know about control of manufacturing systems. Yoram and I had the first digital control computer, a PDP-11, at UM in our laboratory. Michigan was, and is, a wonderful place for control engineering. I had the good fortune to work with, not only Elmer and Yoram, but many outstanding collaborators: Joe Whitesell, the late Pierre Kabamba, Panos Papalambros, Dawn Tilbury, Huei Peng, Ilya Kolmanovsky, Harris McClamroch, Jeff Stein, Gabor Orosz, Chinedum Okwudire and many others! I worked on topics such as automotive belt dynamics, adaptive control of milling, reconfigurable manufacturing, vehicle lane-keeping, co-design of an artifact and its controller, time delay systems, and I was always richer for the experience. Throughout my professional career I worked extensively with industry, especially the Ford Motor Company, where I collaborated with and learned from excellent engineers like Davor Hrovat and Siva Shivashankar (automotive control), Charles Wu (control of drilling), and Mahmoud Demeri (stamping control).

I would like to recognize my wife, Sue Glowski, who is here today, for her love and support. She was educated in English and Linguistics but is always willing to patiently listen to my latest idea about control, even if she has to eventually ask: "what the hell is an eigenvalue?"

Finally, and most importantly, I want to recognize and thank my students and postdocs. This award recognizes your great ideas, and your fine work, and I am delighted to be here today to accept it on your behalf. Thank you!

June 7, 2022
Atlanta, GA USA
ACC 2022

Dear President Braatz, colleagues, students, ladies and gentlemen:

I feel tremendously honored to receive the Richard Bellman Control Heritage Award. Thank you to those who nominated me and supported my nomination, to the selection committee, and to the AACC Board for making me this year’s recipient.

I completed my undergraduate studies at Keio University in Japan and my graduate studies at MIT. Following my education at these wonderful institutions, I was able to join the excellent academic environment at the University of California, Berkeley. I am grateful to my teachers and colleagues at these institutions. I thank in particular my PhD advisor Dan Whitney and my early control colleagues at Berkeley, Yasundo Takahashi and David Aulander, and the many bright graduate students that I have had the privilege of having in my lab at Berkeley who are approximately 120 PhDs strong now. I thank the National Science Foundation and other government sponsors as well as industrial sponsors for providing me resources to maintain the Mechanical Systems Control laboratory, which is the home of my research group. Last but not least, I thank my wife Miwako for supporting me and our family, permitting me to concentrate on academics and schoolwork for many years, starting almost 50 years ago in my MIT days.

I jumped into the area of dynamic systems and control during my senior year at Keio University. The first book I read was Modern Control Theory by Julius Tou. The book was an excellent summary of the State Space Control Theory, and I was fascinated by the elegant mathematical aspects of the subject. There was no internet back then of course, and major periodicals such as IEEE Transactions on Automatic Control and ASME Journal of Basic Engineering were the best sources to find the latest developments in the field. I was frustrated by the time delay between the time of research and publication. About at the time I completed my MS at Keio, I was fortunate to receive an admission offer from MIT. The time delay problem was naturally resolved. At MIT, I was inspired by many people including Dan Whitney, Tom Sheridan and Hank Paynter. Sheridan’s early work on preview control was the starting point of my dissertation work on the “optimal finite preview” problem.

In September 1974, I joined the University of California as an Assistant Professor of Mechanical Engineering. It’s hard to believe, but I am now completing my 44th year at Berkeley.

At Berkeley, I have worked on many different mechanical systems. I joined UC Berkeley when the large scale integration technology was starting to make it possible to implement advanced control algorithms by using mini and micro computers. This allowed me to emphasize both the analytical aspects of control and the laboratory work. This research style still continues now.

Robots are multivariable and nonlinear. In particular, a configuration-dependent inertial matrix and nonlinear terms are unique for robots. I convinced one of my PhD students, Roberto Horowitz (who is now a professor and chair of the Mechanical Engineering Department at Berkeley), to work with me on model reference adaptive control as it applied to robots. Since then, robot control has remained a major research topic in my group. Our current research emphasizes efficiency and safety in human-robot interactions and merging model-based control and machine learning to make the robot system intelligent.

I worked on machining for a while. One control issue with machining is the dependence of input-output dynamics to cutting conditions and tool wear. One day, Jun-Ho Oh (who is now a professor at KAIST), took me down to the lab to show me model reference adaptive control on a Bridgeport milling machine. It was cleverly implemented and was the first application of modern adaptive control theory to machining.

In many mechanical systems involving rotational parts, we encounter periodic disturbances with known periods. Repetitive control is applied to this class of disturbances. I learned of it from visitors from Japan in the mid-1980s. Tsu-Chin Tsao (who is now a professor at UCLA) and I then developed our version of repetitive control algorithms emphasizing discrete time formulation and easy implementation.

Another fundamental control problem for mechanical systems is tracking arbitrary shaped reference inputs. Feedforward control is popular in tracking, but unstable system zeros make the problem complicated. To overcome this issue, I suggested to cancel phase shift induced by unstable zeros and introduced zero phase error tracking (ZPET) control in the late 1980s. The citation of this paper has reached 1,600 by now.

In the mid-1980’s, UC Berkeley started Program on Advanced Transit and Highway under the sponsorship of CalTrans. Automated highway systems was a topic of interest for quite a few control professors. Karl Hedrick and I were the primary faculty participants from ME: Karl worked on controls in the longitudinal direction and I in the lateral direction of vehicles. My first PhD student on this topic was Huei Peng (who is now a professor at University of Michigan). During the past five years or so, autonomous vehicles have become very hot as we all know, and I now have quite a few students working to blend control and machine-learning for applications to vehicles.

I have been fortunate to have had the opportunity to address a variety of challenging mechanical control problems over the span on my career so far. My research has been and continues to be rooted in the mechatronic approach; namely I have worked on the synergetic integration of mechanical systems with sensing, computation, and control theory. This approach provides the opportunity for academic research to have broad impacts on control engineering in practice, and I am honored to have had a hand in helping to advance a small part of it.

Thank you very much for this award. I am extremely grateful and honored.

ACC 2018
Milwaukee, WI USA
June 28, 2018

I am extremely grateful and humbled by being honored to receive the Richard E. Bellman Control Heritage Award for 2016. I thank those that recommended me and the awards committee for supporting that nomination. I also thank my colleagues, students, family and especially my wife for the support I have received over these many years.

For me this award occurs at an auspicious time and place. Boston is the place of my birth and my home. It was sixty years ago that I graduated from Malden High School and entered into a world I could never have anticipated; a world where I would be nurtured for the next twenty years by many people, some of whom have been recipients of this esteemed award.

I enrolled in the Department of Aeronautics at MIT, which after Sputnik became the Department of Aeronautics and Astronautics. In my junior year I entered into the space age. More consequential for me was that the department head was Doc (Charles Stark) Draper[1], whose second volume of his three sequence series on Instrument Engineering (1952) was one the first books on what we know as Classical Control covering such topics as Evens root locus, Bode plots, Nyquist criterion, and Nichols charts. Doc Draper instituted an undergraduate course in classical control that I took my junior year. This inspired me to take a graduate course and write my undergraduate thesis in controls.

After graduation in 1960 I left Boston to work for Boeing in Seattle. There, I worked with my lead engineer Raymond Morth, who introduced me to the new world of control theory using state space that was just emerging in the early 1960’s. I learned of dynamic programming of Richard Bellman for global sufficiency of an optimal trajectory and the Pontryagin Maximum principle inspired by the deficiency of dynamic programing to solve certain classes of optimization problems. The Bushaw problem of determining the minimum time to the origin of a double integrator was just such a problem, since the optimal return function in dynamic programing is not differentiable at the switching curve and the Bellman theory did not apply. Interestingly, for my bachelor’s thesis I applied the results of the Bushaw problem to the minimum time problem of bringing the yaw and yaw rate of an aircraft to the origin. However, at that time I had no idea about the ramification of the Bushaw problem to optimization theory. I also learned of the work of Rudolf Kalman in estimation, the work of Arthur Bryson and Henry Kelley in the development of numerical methods for determining optimal constrained trajectories, and J. Halcombe (Hal) Laning and Richard Battin on the determination of orbits for moon rendezvous.

After an incredible year at Boeing I returned to Boston to work at the Analytical Research Department at Raytheon, where Art Bryson was a consultant. There, I worked with a student of Bryson, Walter Denham. We were contracted by MIT’s Instrumentation Laboratory, monitored by Richard Battin, to enhance the Apollo autonomous navigation system over the trans-Lunar orbit. We developed a scheme for determining the optimal angle-measurement sequence between the best stars in a catalogue and near and far horizons of the Earth or the Moon using a sextant. This angle-measurement sequence minimized some linear function of the terminal value of the error covariance of position and velocity near the Earth or Moon. Our optimization scheme, which required a matrix dynamic constraint, seemed to be a first. This scheme, used in the Apollo autonomous navigation system, was tested on Apollo 8, and used on every mission thereon. My next task at Raytheon was working on neighboring optimal guidance scheme. This work was with Art Bryson and John Breakwell. I remember travelling to Lockheed’s Palo Alto Research Laboratory and meeting with John, the beginning of a long and delightful collegial relationship.

After my first two years at Raytheon I somehow convinced Art Bryson to take me on as a graduate student at Harvard, supported by the Raytheon Fellowship program. To understand the intellectual level I had to contend with, on my doctorial preliminary exam committee, three of the four examiners were recipients of the Richard E. Bellman Control Heritage Award; Art Bryson, Larry (Yu-Chi) Ho, and Bob (Kumpati) Narendra, all of whom have been my life time colleagues. I was also fortunate to take a course taught by Rudy Kalman. Surprisingly, he taught many of the controls areas he had pioneered, except filtering for Gauss-Markov systems (the Kalman filter); the Aizerman conjecture, the Popov criterion and Lyopunov functions, duality in linear systems, optimality for linear-quadratic systems, etc. After finishing my PhD thesis on optimal control problems with state variable inequality constraints, I returned to Raytheon. Fortunately, Art Bryson made me aware of some interest at Raytheon in using modern control theory for developing guidance laws for a new missile. At Raytheon’s Missile Division I worked with Bill O’Halloran on the homing missile guidance system where Bill worked on development of the Kalman filter and I worked on the development of the linear-quadratic closed-form guidance gains that had to include the nonminimal phase autopilot. This homing missile, the Patriot missile system, appears to be the first fielded system using modern control theory.

I left Boston for New York to work at the Analytical Mechanics Associates (AMA), in particular, with Hank Kelley. Although I had a lasting friendship with Hank, I only lasted seven months in New York before returning to the AMA office in Cambridge. Unfortunately, the Cambridge NASA Center closed, and I took a position under Dick Battin at the Instrumentation (later the Charles Stark Draper) Laboratory at MIT. There, I worked on the necessary and sufficient conditions for optimality of singular control problems, the linear-exponential-Gaussian control problem, optimal control problems with state variable inequality constraints, optimal control problems with cost criterion and dynamic functions with kinks, and periodic optimal control problems. On many of these issues I collaborated with David Jacobson, whom I first met in the open forum of my PhD final exam. This remarkable collaboration culminated in our book on optimal control theory that appeared in 2010. Also, during my tenure at Draper, I took a post-doctoral year leave at the Weizmann institute in Israel. Here, I learned that I could work very happily by myself. A few years after returning to Draper, I started what is now a forty year career in academia and I left Boston.

As I look back, I feel so fortunate that I had such great mentoring over my early years and by so many who have won this award. My success over the last forty years has been due to my many students who have worked with me to mold numerous new ideas together. Today, I find the future as bright as anytime in my past. I have embarked in such new directions as estimation and control of linear systems with additive noises described by heavy tailed Cauchy probability density functions with my colleague Moshe Idan at the Technion and deep space navigation using pulsars as beacons with JPL.

To conclude, I am grateful to so many of my teachers, colleagues and students, who have nurtured, inspired, and educated me. Without them and my loving wife and family, I would not be here today. Thank you all.
[1] Boldface names are recipients of the Richard E. Bellman Control Heritage Award.

I feel honored and grateful for this award. After having spent so much time on dynamic programming and written several books about its various facets, receiving an award named after Richard Bellman has a special meaning for me.

It is common in award acceptance speeches to thank one's institutions, mentors, and collaborators, and I have many to thank. I was fortunate to be surrounded by first class students and colleagues, at high quality institutions, which gave me space and freedom to work in any direction I wished to go. As Lucille Ball has told us, "Ability is of little account without opportunity."

Also common when receiving an award is to chart one's intellectual roots and journey, and I will not depart from this tradition. It is customary to advise scholarly Ph.D. students in our field to take the time to get a broad many-course education, with substantial mathematical content, and special depth in their research area. Then upon graduation, to use their Ph.D. research area as the basis and focus for further research, while gradually branching out into neighboring fields, and networking within the profession. This is good advice, which I often give, but this is not how it worked for me at all!

I came from Greece with an undergraduate degree in mechanical engineering, got my MS in control theory at George Washington University in three semesters, while holding a full-time job in an unrelated field, and finished two years later my Ph.D. thesis on control under set membership uncertainty at MIT. I benefited from the stimulating intellectual atmosphere of the Electronic Systems Laboratory (later LIDS), nurtured by Mike Athans and Sanjoy Mitter, but because of my short stay there, I graduated with little knowledge beyond Kalman filtering and LQG control. Then I went to teach at Stanford in a department that combined mathematical engineering and operations research (in which my background was rather limited) with economics (in which I had no exposure at all). In my department there was little interest in control theory, and none at all in my thesis work. Never having completed a first course in analysis, my first assignment was to teach to unsuspecting students optimization by functional analytic methods from David Luenberger's wonderful book. The optimism and energy of youth carried me through, and I found inspiration in what I saw as an exquisite connection between elegant mathematics and interesting practical problems. Studying David Luenberger's other works (including his Nonlinear Programming book) and working next door to him had a lasting effect on me. Two more formative experiences at Stanford were studying Terry Rockafellar's Convex Analysis book (and teaching a seminar course from it), and most importantly teaching a new course on dynamic programming, for which I studied Bellman's books in great detail. My department valued rigorous mathematical analysis that could be broadly applied, and provided a stimulating environment where both could thrive. Accordingly, my course aimed to combine Bellman's vision of wide practical applicability with the emerging mathematical theory of Markov Decision Processes. The course was an encouraging success at Stanford, and set me on a good track. It has survived to the present day at MIT, enriched by subsequent developments in theoretical and approximation methodologies.

After three years at Stanford, I taught for five years in the quiet and scholarly environment of the University of Illinois. There I finally had a chance to consolidate my mathematics and optimization background, through research to a great extent. In particular, it helped a lot that with the spirit of youth, I took the plunge into the world of the measure-theoretic foundations of stochastic optimal control, aiming to expand the pioneering Borel space framework of David Blackwell, in the company of my then Ph.D. student Steven Shreve.

I changed again direction by moving back to MIT, to work in the then emerging field of data networks and the related field of distributed computation. There I had the good fortune to meet two colleagues with whom I interacted closely over many years: Bob Gallager, who coauthored with me a book on data networks in the mid-80s, and John Tsitsiklis, who worked with me first while a doctoral student and then as a colleague, and over time coauthored with me two research monographs on distributed algorithms and neuro-dynamic programming, and a probability textbook. Working with Bob and John, and writing books with them was exciting and rewarding, and made MIT a special place for me.

Nonetheless, at the same time I was getting distracted by many side activities, such as books in nonlinear programming and dynamic programming, getting involved in applications of queueing theory and power systems, and personally writing several network optimization codes. By that time, however, I realized that simultaneous engagement in multiple, diverse, and frequently changing intellectual activities (while not recommended broadly) was a natural and exciting mode of operation that worked well for me, and also had some considerable benefits. It stimulated the cross-fertilization of ideas, and allowed the creation of more broadly integrated courses and books.

In retrospect I was very fortunate to get into methodologies that eventually prospered. Dynamic programming developed perhaps beyond Bellman's own expectation. He correctly emphasized the curse of dimensionality as a formidable impediment in its use, but probably could not have foreseen the transformational impact of the advances brought about by reinforcement learning, neuro-dynamic programming, and other approximation methodologies. When I got into convex analysis and optimization, it was an emerging theoretical subject, overshadowed by linear, nonlinear, and integer programming. Now, however, it has taken center stage thanks to the explosive growth of machine learning and large scale computation, and it has become the lynchpin that holds together most of the popular optimization methodologies. Data networks and distributed computation were thought promising when I got involved, but it was hard to imagine the profound impact they had on engineering, as well as the world around us today. Even set membership description of uncertainty, my Ph.D. thesis subject, which was totally overlooked for nearly fifteen years, eventually came to the mainstream, and has connected with the popular areas of robust optimization, robust control, and model predictive control. Was it good judgement or fortunate accident that steered me towards these fields? I honestly cannot say. Albert Einstein wisely told us that "Luck is when opportunity meets preparation." In my case, I also think it helped that I resisted overly lengthy distractions in practical directions that were too specialized, as well as in mathematical directions that had little visible connection to the practical world.

An academic journey must have companions to learn from and share with, and for me these were my students and collaborators. In fact it is hard to draw a distinction, because I always viewed my Ph.D. students as my collaborators. On more than one occasion, collaboration around a Ph.D. thesis evolved into a book, as in the cases of Angelia Nedic and Asuman Ozdaglar, or into a long multi-year series of research papers after graduation, as in the cases of Paul Tseng and Janey Yu. I am very thankful to my collaborators for our stimulating interactions, and for all that I learned from them. They are many and I cannot mention them all, but they were special to me and I was fortunate to have met them. I wish that I had met Richard Bellman, I only corresponded with him a couple of times (he was the editor of my first book on dynamic programming). I still keep several of his books close to me, including his scintillating and highly original book on matrix theory. I am also satisfied that I paid part of my debt to him in a small way. I have used systematically, for the first time I think in a textbook in 1987, the name "Bellman equation" for the central fixed point equation of infinite horizon discrete-time dynamic programming. It is a name that is widely used now, and most deservedly so.

It is a honor to receive the 2012 Richard E. Bellman Control Heritage Award. I am deeply humbled to join the very distinguished group of prior winners. At this conference there are so many people whose work I have admired for years. To be singled out among this group is a great honor.

I did not know Richard Bellman personally but we are all his intellectual descendants. Years ago, my first thesis problem came from Bellman and currently I am working on numerical solutions to Hamilton-Jacobi-Bellman partial differential equations.

I began graduate school in mathematics at Berkeley in 1964, the year of the Free Speech Movement. After passing my oral exams in 1966, I started my thesis work with R. Sherman Lehman who had been a postdoc with Bellman at the Rand Corporation in the 1950s. Bellman and Lehman had worked on continuous linear programs also called bottleneck problems in Bellman’s book on Dynamic Programming. These problems are dynamic versions of linear programs, with linear integral transformations replacing finite dimensional linear transformations. At each frozen time they reduce to a standard linear program. Bellman and Lehman had worked out several examples and found that often the optimal solution was basic, at each time an extreme point of the set of feasible solutions to the time frozen linear program. These extreme points moved with time and the optimal solution would stay on one moving extreme point for awhile and then jump to another. It would jump from one bottleneck to another.

Lehman asked me to study this problem and find conditions for this to happen. We thought that it was a problem in functional analysis and so I started taking advanced courses in this area. Unfortunately, about a year later Lehman had a very serious auto accident and lost the ability to think mathematically for some time. I drifted, one of hundreds of graduate students in Mathematics at that time. Moreover, Berkeley in the late 1960s was full of distractions and I was distractable. After a year or so Lehman recovered and we started to meet regularly. But then he had a serious stroke, perhaps as a consequence of the accident, and I was on my own again.

I was starting to doubt that my thesis problem was rooted in functional analysis. Fortunately, I had taken a course in differential geometry from S. S. Chern, one of the pre-eminent geometers of his generation. Among other things, Chern had taught me about the Lie bracket. And one of my graduate student colleagues told me that I was trying to prove a bang-bang theorem in Control Theory, a field that I had never heard of before. I then realized that my problem was local in nature and intimately connected with flows of vector fields so the Lie bracket was an essential tool. I went to Chern and asked him some questions about the range of flows of multiple vector fields. He referred me to Bob Hermann who was visiting the Berkeley Physics Department at that time.

I went to see Hermann in his cigar smoked-filled office accompanied by my faithful companion, a German Shepherd named Hogan. If this sounds strange, remember this was Berkeley in the 1960s. Bob was welcoming and gracious, he gave me galley proofs of his forthcoming book which contained Chow’s theorem. It was almost the theorem that I had been groping for. Heartened by this encounter I continued to compute Lie brackets in the hope of proving a bang-bang theorem.

Time drifted by and I needed to get out of graduate school so I approached the only math faculty member who knew anything about control, Stephen Diliberto. He agreed to take me on as a thesis student. He said that we should meet for an hour each week and I should tell him what I had done. After a couple of months, I asked him what more I needed to do to get a PhD. His answer was “write it up”. My “proofs” fell apart several times trying to accomplish this. But finally, I came up with a lemma that might be called Chow’s theorem with drift that allowed me to finish my thesis.

I am deeply indebted to Diliberto for getting me out of graduate school. He also did another wonderful thing for me; he wrote over a hundred letters to help me find a job. The job market in 1971 was not as terrible as it is today but it was bad. One of these letters landed on the desk of a young full professor at Harvard, Roger Brockett. He had also realized that the Lie bracket had a lot to contribute to control. Over the ensuing years, Roger has been a great supporter of my work and I am deeply indebted to him.
Another Diliberto letter got me a position at Davis where I prospered as an Assistant Professor. Tenure came easily as I had learned to do independent research in graduate school. I brought my dog, Hogan, to class every day, he worked the crowds of students and boosted my teaching evaluations by at least a point. After 35 wonderful years at Davis, I retired and joined the Naval Postgraduate School where I continue to teach and do research. I am indebted to these institutions and also to the NSF and the AFOSR for supporting my career.

I feel very fortunate to have discovered control theory both for the intellectual beauty of the subject and the numerous wonderful people that I have met in this field. I mentioned a few names, let me also acknowledge my intellectual debt to and friendship with Hector Sussman, Petar Kokotovic, Alberto Isidori, Chris Byrnes, Steve Morse, Anders Lindquist, Wei Kang and numerous others.

In my old age I have come back to the legacy of Bellman. Two National Research Council Postdocs, Cesar Aguilar and Thomas Hunt, have been working with me on developing patchy methods for solving the Hamilton-Jacobi-Bellman equations of optimal control. We haven’t whipped the “curse of dimensionality” yet but we are making it nervous.

The first figure shows the patchy solution of the HJB equation to invert a pendulum. There are about 1800 patches on 34 levels and calculation took about 13 seconds on a laptop. The algorithm is adaptive, it adds patches or rings of patches when the residual of the HJB equation is too large. The optimal cost is periodic in the angle. The second figure shows this. Notice that there is a negatively slanted line of focal points. At these points there is an optimal clockwise and an optimal counterclockwise torque. If the angular velocity is large enough then the optimal trajectory will pass through the up position several times before coming to rest there.

What are the secrets to success? Almost everybody at this conference has deep mathematical skills. In the parlance of the NBA playoffs which has just ended, what separates researchers is “shot selection” and “follow through”. Choosing the right problem at the right time and perseverance, nailing the problem, are needed along with good luck and, to paraphrase the Beatles, “a little help from your friends”.

I am exceedingly happy to receive the Richard Bellman Control Heritage Award. I am thankful to the American Automatic Control Council for recognizing my work as worthy of this award, and I am deeply humbled when I consider the previous recipients of the award.

My first thanks go to my dear wife Dragana who put up for a long time with a workaholic husband with an oversized ambition. I am grateful to Santa Clara University and, in particular, to the School of Engineering for providing institutional support to our research. I am exceedingly thankful to many people from all around the world who came to Santa Clara to work on our projects as fellow researchers on an exploratory journey; and what a journey it has been!

At this occasion, it gives me a great pleasure to recall my visit to University of Southern California and my brief encounter with Professor Bellman. After my talk, he invited me to his office, and among myriad of his interests, he chose to talk with me about his recent work in Pharmacokinetics. At that time, I was deeply into the competitive equilibrium in economics, and we had a very stimulating discussion on the connection of the two fields via the Metzler matrix which I have been using since then in a wide variety of models to this very day.

Looking at this award in a prudential light, my obtaining this award is as much a compliment to the Control Council as it is to me. My winning of this award at Santa Clara University, which is not a research 1 university but prides itself as an excellent teaching institution, proves that the system is open, and that any of you wherever you are can win this award solely by the merit of your research.

I recall when at eighteen I made the Yugoslav Olympic Water Polo Team for the 1952 Helsinki Olympic Games. We won all our games except the final one, which ended in a draw. At that time, there were no overtimes and penalty kicks; the winner was determined by the cumulative goal ratio. I continued playing water polo, but did not make the team for the 1956 Melbourne games; I broke my right hand and stayed home. I kept playing on and in 1960 made the team for the Rome Olympics. We did not win a medal in Rome, let alone the gold. At that point I was already a committed researcher in control systems.

I continued the research for many years and to borrow from a song by Neil Young:

"I kept searching for a heart of gold, and I was getting old ... "
Today I found a heart of gold. Thank you all very much for your attention, and God bless!

July 1, 2010. Baltimore, MD

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.

Stochastic Systems
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.

Networking
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.

Power
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.

Wireless
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.

Hybrid
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.

Transportation
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.
June 12, 2008. Seattle, WA

I am honored to receive this most prestigious award and recognition by the American Automatic Control Council, named after Richard Ernest Bellman (the creator of "dynamic programming")---who has shaped our field and influenced through his creative ideas and voluminous multifaceted work the research of tens of thousands, not only in control, but also in several other fields and disciplines. In my own research, which has encompassed control, games, and decisions, I have naturally also been influenced by the work of Bellman (on dynamic programming), as well as of Rufus Isaacs (the creator of differential games) whose tenure at RAND Corporation (Santa Monica, California) partially overlapped with that of Bellman in the 1950s. I want to use the few minutes I have here to say a few words on those early days of control and game theory research (just a brief historical perspective), and Bellman's role in that development.

In a Bode Lecture I delivered (at the IEEE Conference on Decision and Control in the Bahamas) in December 2004, I had described how modern control theory was influenced by the research conducted and initiatives taken at the RAND Corporation in the early 1950s. RAND had attracted and housed some of the great minds of the time, among whom was also Richard Bellman, in addition to names like Leonard D. Berkovitz, David Blackwell, George Dantzig, Wendell Fleming, M.R. Hestenes, Rufus Isaacs, Samuel Karlin, John Nash, J.P. LaSalle, and Lloyd Shapley (to list just a few). These individuals, and several others, laid the foundations of decision and game theory, which subsequently fueled the drive for control research. In this unique and highly conducive environment, Bellman started working on multi-stage decision processes, as early as 1949, but more fully after 1952---and it is perhaps a lesser known historical fact that one of the earlier topics Bellman worked on at RAND was ! game theory (both zero- and nonzero-sum games) on which he co-authored research reports with Blackwell and LaSalle. In an informative and entertaining autobiography he wrote 32 years later ("Eye of the Hurricane", World Scientific, Singapore), completed in 1984 shortly before his untimely death (March 19), Bellman describes eloquently the research environment at RAND and the reason for coining the term "dynamic programming".

At the time, the funding for RAND came primarily from the Air Force, and hence it was indirectly under the Secretary of Defense, who was in the early 1950s someone by the name Wilson. According to Bellman, "Wilson had a pathological fear and hatred of the word 'research' and also of anything 'mathematical' ". Hence, it was quite a challenge for Bellman to explain what he was doing and interested in doing in the future (which was research on multi-stage decision processes) in terms which would not offend the sponsor. "Programming" was an OK word; after all Linear Programming had passed the test. He wanted "to get across the idea that what he was doing was dynamic, multi-stage, and time-varying", and therefore picked the term "Dynamic Programming". He thought that "it was a term not even a Congressman could object to". This being the official reason given for his pick of the term, some say (Harold Kushner--recipient of this award two years ago--being one of them, based on a personal conversation with Bellman) that he wanted to upstage Dantzig's Linear Programming by substituting "dynamic" for "linear". Whatever the reasons were, the terminology (and of course also the concept and the technique) was something to stay with us for the next fifty plus years, and undoubtedly for many more decades into the future, as also evidenced by the number of papers at this conference using the conceptual framework of dynamic programming.

Applying dynamic programming to different classes of problems, and arriving at "functional equations of dynamic programming", subsequently led Bellman, as a unifying principle, to the "Principle of Optimality", which Isaacs, also at RAND, and at about the same time, had called "tenet of transition" in the broader context of differential games, capturing strategic dynamic decision making in adversarial environments.

Bellman also recognized early on that a solution to a multi-stage decision problem is not merely a set of functions of time or a set of numbers, but a rule telling the decision maker what to do, that is, a "policy". This led in his thinking, when he started looking into control problems, to the concept of "feedback control", and along with it to the notions of sensitivity and robustness. These developments, along with the more refined notions of information structures (who knows what and when), have been key ingredients in my research for the past thirty plus years.

It is interesting that at RAND at the time (that is in the 1950s), in spite of the anti-research and anti-mathematical attitude that existed in the higher echelons of the government, and the Department of Defense in particular, fundamental research did prosper, perhaps somewhat camouflaged initially, which in turn drove the creation of modern control theory, fueled also by the post-Sputnik anxiety. There is perhaps a message that should be taken from that: "Don't give up doing what you think and believe is right and important, but also be flexible and accommodating in how you promote it".

Before closing, I want to thank all who have been involved in the nomination process and the selection process of the Bellman Control Heritage Award this year. I want to use this occasion also to acknowledge several educational and research institutions which have impacted my life and career.

First, I want to acknowledge the contributions of the educational institutions in my native country, Turkey, in the early years of my upbringing, and the comfortable research environment provided by the Marmara Research Institute I was affiliated with in the mid to late 1970s. Second, I want to acknowledge the love for research and the drive for pushing the frontiers of knowledge I was infected with during my years at Yale and Harvard in the early 1970s. And last, but foremost, I want to acknowledge the perfect academic environment I found and have still been enjoying at the University of Illinois at Urbana-Champaign---wonderful colleagues, stimulating teaching environment at the Department of Electrical and Computer Engineering, and exemplary conducive research environment at the Coordinated Science Laboratory with its top quality graduate students. I also want to recognize all students, post-docs, and colleagues I have had the privilege of having research interactions and collaborations with over the years. I thank them all for the memorable journeys in exploring the frontiers in control science and technology.

Thank you very much.
June 15, 2006. Minneapolis, MN
June 15, 2006. Minneapolis, MN

It is a great honor to receive this award. It is a particular honor that it is in memory of Richard Bellman. I doubt that there are many here who knew Bellman, so I would like to make some comments concerning his role in the field.

Bellman left RAND after the summer of 1965 for the position of Professor of Electrical Engineering, Mathematics, and Medicine at the University of Southern California. This triple title gives you some inkling of how he was viewed at the time. I spent that summer at RAND. My office was right next to Bellman's and we had lots of opportunity to talk.

Bellman was always very supportive of my work. He encouraged me to write my first book, Stochastic Stability and Control, in 1967 for his Academic Press Series. Although naive by modern standards, the book seemed to have a significant impact on subsequent development in that it made many mathematicians realize that there was serious probability to be done in stochastic control, and established the foundations of stochastic stability theory. Numerical methods were among his strong interests. He was well acquainted with my work on numerical methods for continuous time stochastic systems and encouraged me to write my first book on the subject, later updated in two books with Paul Dupuis, and still the methods of choice. Despite his enormous output of published papers, something like 900, he was a strong believer in books since they allowed one to develop a subject with considerable freedom.

There are other connections, albeit indirect, between us. He was a New Yorker, and did his early undergraduate work at CCNY. During those years and, indeed, until the late 50's, CCNY was one of the most intellectual institutions of higher learning in the US. During that time, before the middle class migration out of the city, and the simultaneous opening of opportunities in the elite institutions for the "typical New Yorker," CCNY had the choice of the best of New Yorkers with a serious intellectual bent. Later, he switched to Brooklyn College, which was much closer to his home.

He intended to be a pure mathematician: His primary interest was analytic number theory. When did he become interested in applications? He graduated college at the start of WW2 and the demands of the war exposed him to a great variety of problems. He taught electronics in Princeton and then worked at a sonar lab in San Diego (which kept him out of the Army for a while). He spent the last two years of the war in the army, but assigned to the Manhattan project at Los Alamos. He was a social creature and it was easy for him to meet many of the talented people working on the project. Typically, the physicists considered a mathematician as simply a human calculator, ideally constructed to do numerical computations but not much more. Bellman was asked to numerically solve some PDE's. His mathematical pride refused. To the great surprise of the physicists, he actually managed to integrate some of the equations, obtaining closed form solutions. Holding true to tradition, they checked his solutions, not by verifying the derivation, but by trying some very special cases. Thus his reputation there as a very bright young mathematician was established. This jealously guarded independence and self confidence (and lack of modesty) continued to serve him well. During these years, he absorbed a great variety of scientific experiences. So much was being done due to the needs of the war.

There is one more indirect connection between us. Bellman was a student of Solomon Lefschetz at Princeton, head of the Math. Dept. at the time, a very tough minded mathematician and one of the powerhouses of American mathematics, and impressed with Bellman's ability. While at Los Alamos in WW2 Bellman worked out various results on stability of ODE's. Although he initially intended to do a thesis with someone else on a number theoretic problem, Lefschetz convinced him that those stability results were the quickest way to a thesis, which was in fact true. It took only several months and was the basis of his book on stability of ODE's. I was the director of the Lefschetz Center for Dynamical Systems at Brown University for many years, with Lefschetz our patron saint. Some of you might recall the book (not the movie) "A Beautiful Mind" about John Nash, a Nobel Laureate in Game Theory, which describes Lefschetz's key role in mathematics during Nash's time at Princeton.

Bellman spent the summer of 1948 at RAND, where an amazing array of talent was gathered, including David Blackwell, George Dantzig, Ted Harris, Sam Karlin, Lloyd Shapley, and many others, who provided the foundations of much of decision and game theory. The original intention was to do mathematics with some of the RAND talent on problems of prior interest. But Bellman turned out to be fascinated and partially seduced by the excitement in OR, and the developing role of mathematics in the social and biological sciences. His mathematical abilities were widely recognized. He was a tenured Associate Professor at Stanford at 28, after being an Associate Professor at Princeton, where all indications were that he would have had an assured future had he remained there. He began to have doubts about the payoff for himself in number theory and returned to the atmosphere at RAND often, where he eventually settled and became fully involved in multistage decision processes, having been completely seduced, and much to our great benefit.

Here is a non mathematical item that should be of interest. To work at RAND one needed a security clearance, even though much of the work did not involve "security." Due to an anonymous tip, Bellman lost his clearance for a while: His brother-in-law, whom Bellman had not seen since he (his brother-in-law) was about 13, was rumored to be a communist? This was an example of a serious national problem that was fed, exploited, and made into a national paranoia by unscrupulous politicians.

Bellman was a remarkable person, thoroughly a man of his time and renaissance in his interests, with a fantastic memory. Some epochs are represented by individuals that are towering because of their powerful personalities and abilities. People who could not be ignored. Bellman was one of those. He was one of the driving forces behind the great intellectual excitement of the times.

The word programming was used by the military to mean scheduling. Dantzig's linear programming was an abbreviation of "programming with linear models." Bellman has described the origin of the name "dynamic programming" as follows. An Assistant Secretary of the Air Force, who was believed to be strongly anti-mathematics was to visit RAND. So Bellman was concerned that his work on the mathematics of multi-stage decision process would be unappreciated. But "programming" was still OK, and the Air Force was concerned with rescheduling continuously due to uncertainties. Thus "dynamic programming" was chosen a politically wise descriptor. On the other hand, when I asked him the same question, he replied that he was trying to upstage Dantzig's linear programming by adding dynamic. Perhaps both motivations were true.

If one looks closely at scientific discoveries, ancient seeds often appear. Bellman did not quite invent dynamic programming, and many others contributed to its early development. It was used earlier in inventory control. Peter Dorato once showed me a (somwhat obscure) economics paper from the late thirties where something close to the principle of optimality was used. The calculus of variations had related ideas (e.g., the work of Caratheodory, the Hamilton-Jacobi equation). This led to conflicts with the calculus of variations community. But no one grasped its essence, isolated its essential features, and showed and promoted its full potential in control and operations research as well as in applications to the biological and social sciences, as did Bellman.

Bellman published many seminal works. It is sometimes claimed that many of his vast number of papers are repetitive and did not develop the ideas as far as they could have been. Despite this criticism, his works were poured over word for word, with every comment and detail mined for ideas, technique, and openings into new areas. His work was a mother lode. It was clearly the work of someone with a superb background in analysis as well as a facile mind and sharp eye for aplications. There are lots of examples, with broad coverage, accessible, and usually simple assumptions. His writing is articulate. It flows very smoothly through the problem formulation and mathematical analysis, and he is in full command of it.

We still owe a great debt to him.
July 1, 2004. Boston, MA

I am immensely pleased by the Award! It is indeed a special honor, coming from the American Automatic Control Council, which has done so much to advance and to unify the field of control. I recall with delight the long sequence of Joint Automatic Control Conferences and the subsequent American Control Conferences. The Council's many current activities, including its participation in this 13th IFAC World Congress, continue its invaluable service to the control community.

In receiving the award I wish to recognize the support of friends, colleagues and former students. They have played a vital role in my work. I must also acknowledge the special influence of others I have known mostly or entirely through their publications. It is no surprise that Richard Bellman was one of them. Let me make a few remarks about his legacy and how it affects us today.

In examining his writings I am struck by his genuine interest in applications and obvious desire to make his findings useful to a wide audience. In this, I believe, there are lessons to be learned. I'll note four.

1. Fundamental ideas have greater power when they are elegantly expressed. There is no better example than Bellman's formulation of dynamic programming. Its wonderfully stated ideas permeate and illuminate much of what we do, ranging from deep theoretical results in optimal control to practical, on-line implementation of controllers.

2. Propagation of knowledge is enhanced by the establishment of connections across fields and disciplines. Bellman's 1960 book, "Introduction to Matrix Analysis," illustrates this point beautifully. The discussions and bibliographies and the end of each chapter are marvelous sources of insight and diversity.

3. In mathematical exposition, clarity and accessibility are precious attributes. Bellman had a special talent for keeping mathematical developments closely connected to first principles and organizing them in simple, easy to understand parcels. He had the courage to compromise generality for clarity and, on occasion, rigor for insight.

4. Numerical issues are crucial to control applications. Bellman realized this early, four decades ago, when he addressed controller implementation, algorithm design, error analysis, and computational complexity.

Over the years the field of control has become mature, complex and diverse. We now need, as Richard Bellman did so well, to give greater attention to the means by which we encourage its progress and impact on society. On that point I will end.
Thank you.

July 4, 1996