Roger Ware Brockett, 84, Pioneering Control Theorist and Founder of the Harvard Robotics Laboratory

by Louise Brewster Brockett

            — Photo credit: Eliza Grinell

Roger Ware Brockett, the An Wang Professor of Electrical Engineering and Computer Science, Emeritus, at Harvard University, who grew up on a farm in Ohio and went on to become one of the most lauded applied scientists of his generation, died at Yale New Haven Hospital early on the morning of Sunday, March 19, 2023. He was 84. The cause of death was complications from a fall last October at his home in Lexington, Massachusetts, according to his wife of sixty-two years, Carolann Riske Brockett.

Professor Brockett taught at Harvard for forty-two years, having joined the faculty in 1969 as Gordon McKay Professor of Applied Mathematics in the Division of Engineering and Applied Physics, following six years as a Ford Foundation fellow, assistant professor, and associate professor of electrical engineering at the Massachusetts Institute of Technology. While at Harvard, he became widely celebrated for his pioneering contributions to automatic control. He laid the foundations for geometric nonlinear control in the 1970s, providing seminal insights into the mathematical tools that would be needed to extend the linear methods of the era into the nonlinear domain. His research inspired a generation of mathematicians that included Arthur Krener, Alberto Isidori, and Hector Sussmann, who worked with him in creating the differential geometric methods on which the modern theory of nonlinear systems, feedback linearization, stabilization, and nonlinear filtering are based. He was the author or co-author of several hundred scholarly papers and a classic textbook, Finite Dimensional Linear Systems, published by Wiley in 1970.

Upon learning of Professor Brockett's death, Frank Doyle, Dean, Harvard School of Engineering and Applied Sciences, remarked, "Over a career that spanned nearly fifty years, Roger had an incredible impact on students through his lecturing on engineering design as well as his mentoring of more than sixty Ph.D. students. His foundational work on differential geometric control methods for nonlinear systems continues to inform and inspire those working on the design of feedback linearization-based controllers across a range of applications. He also led the field with one of the earliest contributions, in 2000, to the now expanding field of quantum control systems." Added Yu-Chi Larry Ho, Gordon McKay Professor of Systems Engineering, Emeritus and T. Jefferson Coolidge Professor of Applied Mathematics, Emeritus, "Professor Brockett covered a wide spectrum of research in control theory. He was not content to work within the newly established framework of control research; he went on to establish new frameworks and foundational systems."

In 1983, Roger Brockett founded the Harvard Robotics Laboratory, ushering Harvard to the forefront of a field poised for explosive growth and conducting groundbreaking research on robotic manipulation, formal languages for motion description, computer vision, and optimal control of Markov processes. In 1989, he was named the An Wang Professor of Electrical Engineering and Computer Science at the university's division now known as the John A. Paulson School of Engineering and Applied Sciences. A 2011 announcement by the university, upon the occasion of his receiving the Capers and Marion McDonald Award for Excellence in Mentoring and Advising, stated that "publications by Brockett and his students have defined entirely new areas of research" David Dobkin, now Phillip Y Goldman `86 Professor of Computer Science, Emeritus, at Princeton, noted then that "Every so often, Roger would see a piece of mathematics or a derived result that was so elegant that he couldn't help himself. He'd circle the result on his chalkboard and write "Truth and Beauty." Professor Brockett retired from teaching in 2011, assuming his emeritus position at Harvard but continuing to conduct research, publish papers, and present lectures at institutions around the globe.

During his career, Professor Brockett taught both graduate and undergraduate students. Many of his sixty-two doctoral advisees (approximately fifty of them at Harvard and the others at MIT and Brandeis) became leading professors in their fields, including John Baillieul of Boston University, John Baras and P.S. Krishnaprasad of University of Maryland, Mohammed Belabbas and Daniel Liberzon of University of Illinois, Urbana-Champaign, Anthony Bloch of University of Michigan, Douglas Cochran and Tom Taylor of Arizona State University, Professor Dobkin of Princeton, Abdol-Reza Mansouri of Queens University at Kingston, Kristi Morgansen of University of Washington, the late Jan Willems of University of Groningen, Alan Willsky of MIT, Wing Shing Wong of Chinese University of Hong Kong, and many others.

Speaking at Professor Brockett's funeral service at Memorial Church, Harvard University, on Tuesday, March 28, Harry R. Lewis, Gordon McKay Research Professor of Computer Science, former Dean of Harvard College, and a longtime colleague and friend of Professor Brockett's, reflected, "in Roger Brockett, small-town Ohio met the world. . . . Students by the dozens came to study under him from the four corners of the earth, and then moved onwards, or returned, each bearing a piece of Roger's soul to sow the gardens of their own universities. And through it all, Roger never lost his Midwestern accent, reserve, and humility, his delight in the underlying simplicity of complicated phenomena, or the kindness and joy he could take in everyday things. Powerful as his intellect was, the schoolboy spirit stayed with him always. He inspired his students by having fun with them."

Some of those former students spoke at Professor Brockett's service or at the reception that followed at the Harvard Faculty Club. Professor John Baillieul related during the service that when he first came to study at Harvard, he "had not a clue what control theory was, but it looked interesting. . . . I wanted to study geometry, and he was inventing geometric control theory. Roger was very personal in his teaching style. He would come in and say he was the 'theorem monster; he needs to be fed theorems'. He did this every day. Roger continued to be a mentor to all of us as the years went by. He would always call to check in. Our families became his family, and his family became ours. It was a precious, great ride."

Professor John Baras of University of Maryland commented during the reception, "Roger was one of the last few remaining polymaths. He persistently linked, fluently, ideas and concepts from physics, chemistry, engineering, systems, control, optimization, biology, computational models and complexity, and quantum mechanics. A few seminal and famous examples are his introduction of Lie algebras in nonlinear systems, his breakthrough contributions to efficient matrix multiplication, his unexpected demonstration of solving combinatorial problems via analog computation, his deep work connecting stochastic control with key aspects of thermodynamics, and his novel time optimal control of NMR spin systems." Professor Baras also pointed to Professor Brockett's "balance between theory and practice" and his love of "gadgetry," as demonstrated by his innovations with the robotic hand. "He was one of the first to imagine and create a hand that had flexible fingers, and he was able to touch very minute dimensions while playing around with the flexibility of the fingers."

A. Stephen Morse, Dudley Professor of Electrical Engineering at Yale and a longtime friend, offered the warm reflection, "He was an engineer down to his toenails. If you knew him well, the guy was really an engineer. He loved mathematics; he loved the beauty of mathematics; he loved the structure…but what he really liked was the utility of mathematics — being able to use it to solve the kinds of problems that he was interested in solving. I'll make an analogy. Suppose that Roger was an essayist. He would love the structure of the essay, the vocabulary, the grammar, the rhythm, but he would like most what the essay said. That's Roger Brockett."

In addition to his work with graduate students, Professor Brockett welcomed undergraduate researchers to his robotics laboratory, occasionally supervising their honors theses. He created or co-created two popular undergraduate engineering courses: ES 50, Introduction to Electrical Engineering, and ES 51, Computer-Aided Machine Design. He also served as associate director of the Brown-Harvard-MIT Center for Intelligent Control Systems and collaborated with researchers at the University of Maryland through the Maryland-Harvard National Science Foundation Engineering Research Center on Systems Engineering (a collaboration which, explained Professor Baras, Professor Brockett worked to establish, and which was “a natural outgrowth of his visionary and cross-disciplinary thinking and ideas”). He also served on advisory committees for the Institute of Electrical and Electronics Engineers (IEEE), the Society for Industrial and Applied Mathematics (SIAM) and the American Mathematical Society (AMS), and as a consultant to MIT's Lincoln Laboratory. He was invited to be a guest teacher at universities worldwide, including Australian National University, Ben Gurion University, Imperial College, Tokyo Institute of Technology, Warwick University, and the Universities of Bremen, Groningen, Nagoya, and Rome, among others.

Roger Ware Brockett was born on October 22, 1938, in Wadsworth, Ohio, the youngest of seven children of Roger Lawrence Brockett, a farmer, and Grace Esther (Patch) Brockett, a first-grade teacher. His first home, in Westfield Township, Ohio, had no electricity and only two bedrooms for a family of nine. By the time he was ten, the family had moved twice, down the same county road, to a bigger farm in Seville. Starting in sixth grade, he took turns with his father and brothers, each July through November, sleeping alone in a small shed in the middle of the free-range field for the farm’s 1500 turkeys, to keep the foxes at bay. He learned to drive by age twelve so that he could deliver his mother to work before going to school himself. And when a sibling altercation (over a football kicked into the farm’s silo) resulted in a pitchfork accidentally lodged in his calf, he pulled it out and carried on with the day. There was time, however, to compete on the Akron broadcast of the radio program "Quiz Kids" and to acquaint himself with the engine of his father's Farmall tractor. Noted Professor Brockett recently, "Even though I lived very closely with animals every day, I found machines more interesting."

While in eighth grade, he got to know a sixth grader, Carolann Christina Riske, who played clarinet with him in the school band. After dating on and off for years, they would marry on August 20, 1960, following his senior and her sophomore year of college.

He went to Case Institute of Technology (now Case Western Reserve University), where he completed three degrees in eight years, picking up varsity letters in football and basketball along the way. He received his B.S. in engineering science in 1960, his M.S. in 1962, and his Ph.D. in 1964. His dissertation, under adviser Mihajlo D. Mesarovic, was "The Invertibility of Dynamic Systems with Application to Control."

In 1963, shortly before completing his doctorate, he happened to have a conversation with Peter Elias, then chairman of the electrical engineering department at MIT, whom Mesarovic had invited to Case to give a lecture. Shortly after that conversation, a letter arrived from MIT offering Brockett an assistant professorship there. He and his wife moved east, soon settling in Lexington, where they would remain and rear three sons. Though far removed from the farm, Professor Brockett maintained his "early to rise" ethic, waking each day by dawn to tackle math problems with pad and pen.

During his career, Professor Brockett received three major awards for teaching: the IEEE's Leon K. Kirchmayer Graduate Teaching Award (2009) for his "inspirational mentoring of generations of graduate students who have gone on to define the field of control engineering," the McDonald Award, and the 2014 John R. Ragazzini Education Award of the American Automatic Control Council. Additionally, he was named a fellow of IEEE in 1974, a John Simon Guggenheim fellow (1976-1977), and a fellow of the American Mathematical Society in 2012; he was elected to the National Academy of Engineering in 1991. He received the Donald P. Eckman Award (1967) and the Richard E. Bellman Control Heritage Award (1989) from the American Automatic Control Council, the IEEE Control Systems Science and Engineering Award (1991), the W. T. and Idalia Reid Prize in Mathematics from the Society for Industrial and Applied Mathematics (1996), the Rufus Oldenburger Medal from the American Society of Mechanical Engineers (2005), and the International Federation of Automatic Control (IFAC) Giorgio Quazza Medal for lifetime achievement (2017).

Professor Brockett recalled in an oral history interview conducted by Professor Baillieul in 2021 for the IEEE History Center that, given his field of research, he had been asked over the years why he had left an engineering-focused university for Harvard. He explained, "I think one thing that people need to understand is that if you put too much like-minded expertise in a small space, you encourage people to become narrow. And if they have room to expand like a nice gas in an open container, then they can explore various parts of the universe that they might otherwise not. And I think I lived that."

In addition to his wife, he is survived by his son Douglas of Menlo Park, California, Douglas's wife, Rei (Chen), and their children, Roger Jensen, Jane, and Helen; his son Erik of New York City; his daughter-in-law Louise (Brewster) Brockett of New York City and her children, William, John, Thomas, and Roger Ware II; and his brother Richard, of Garrettsville, Ohio, and his wife, Mary Ann (Ross). His eldest son, Mark, of New York City, predeceased him.

A Brockett Endowment to support activities that were central to Roger Brockett's life-long interest in scholarship has been set up and is accessible here.