George Leitmann is a Professor Emeritus of engineering science and associate Dean for International Relations at the University of California, Berkeley. His 50+year Berkeley career has included everything from research and teaching to serving as the first ombudsman in the UC system. During seven years at the US Naval Ordnance Test Station, China Lake, he worked mostly on rocket trajectory optimization and testing. He joined the Berkeley faculty in 1957. With the beginning of his appointment at UC in 1957 he began to extend his work in variational calculus and optimal control theory, both in theory and applications, some of which is contained in an introductory text (1967) and two edited volumes (1965 and '69), later expanded to a basic text (1981). This work was awarded the Goddard aerospace and the flight mechanics awards of the American Institute of Aeronautics and Astronautics. That in turn led to research in dynamical game theory and its applications, which can be found in three books (1966, 1967 and 1974) and numerous edited volumes. In the early 1970's and extending into the 1990's, this led to research on robust control with applications to uncertain systems in engineering, science, economics and management for which he was awarded the Levy medal of the Franklin Institute and more recently the first Isaacs Award of the International Society of Dynamic Games. He is a member of the National Academy of Engineering as well as of six foreign academies of science and engineering, and he holds three honorary doctorates. Since emeritation in 1991, he has returned to earlier work in the calculus of variations, especially numerous extensions of a 1967 paper, which are based on the methodology of equivalent problem solutions and regularizing transformations, which simplify the classical approach of Caratheodory. Lately, he has also turned to topics of more recent interest such as an analysis of the dynamics of terrorism. Professionally, he edited or co-edited over a dozen journals including the largest and arguably the most prestigious journal of mathematical analysis and applications founded by Richard Bellman, the latter as editor for sixteen years. Since so many of Professor Leitmann's doctoral students and post-doctoral fellows were international ones and his interests always transcended the US border, he became very involved with international collaborations, was awarded an Alexander von Humboldt Prize in 1980 and subsequently the A. von Humboldt medal and the Werner Heisenberg medal of the A. von Humboldt Foundation.
June 11, 2009. St. Louis, MO
First of all, I wish to express my sincere thanks to the American Automatic Control Council for bestowing on me the Bellman Control Heritage Award. This great honor was completely unexpected so that my gratitude is very deep indeed. I would like to use this rare opportunity to say a few words about a topic which has concerned me for some time, namely, the question Who did what first?. In so doing, I shall relate two examples of which the first is especially a propos since it involves the patron of the award, Richard Bellman, as well as Rufus Isaacs, both long-time friends of mine. When I attended the 1966 International Congress of Mathematicians in Moscow, where Dick was a plenary speaker and Rufus was to present a paper entitled Differential games and dynamic programming, and what the latter can learn from the former, the meeting was buzzing with excitement about an upcoming confrontation between two well known American mathematicians. And indeed, when Rufus presented his paper it was his take on the discovery of the Principle of Optimality which, in his view, appeared after the in-house publication of three RAND reports on differential games, and which appeared to be just a one-player version of his Tenet of Transition. The result of this implied accusation of plagiarism had two unhappy consequences. I had lunch with Dick on that day. He was deeply hurt, so much so that he was near tears. Equally unfortunate was the effect on Rufus who devoted much of his remaining time to trying to prove the priority of his discovery instead of continuing to produce new and important research of which his fertile mind was surely capable. The second example is a much happier one. In the mid-1960's I published a brief paper in which I proposed constructive sufficiency conditions for extremizing a class of integrals by solving an equivalent problem by inspection. It was not until 1999 that I returned to this subject at the urging of a Canadian colleague. After revisiting the original 1967 paper, I published a generalization in JOTA in 2001. On presenting these results at my 75th birthday symposium in Sicily in 2001, Pierre Bernhard remarked that my approach seemed to be related to Caratheodory's in his 1935 text on the calculus of variations and partial differential equations, first translated into English in the mid-1960's and not known to me. And indeed, in 2002, Dean Carlson published in JOTA a paper in which he discussed a relation between the two approaches in that both are based on the equivalent problem methodology. Caratheodory obtained an equivalent problem by allowing for a different integrand, and I obtained an equivalent problem by the use of transformed variables. Dean then proposed a generalization by combining the two approaches. A happy consequence of this paper has been and continues to be a fruitful collaboration which has resulted in many extensions and applications, e.g., to classes of optimal control and differential game problems, to multiple integrals, and to economic problems, the most recent concerned with differential constraints (state equations) and presented just a couple of weeks ago at the 15th International Workshop on Dynamics and Control. A particularly interesting discussion and some generalizations by Florian Wagener may be found in the July 2009 issue of JOTA. Thus, Caratheodory received his well deserved citation and I learned a great deal, allowing me to make some small contributions to optimization theory.