Roger Brockett, pioneer of the union between engineering and mathematics, dies | Sciences

Roger Brockett, a Harvard professor whose contributions left a lasting mark on the world of engineering and mathematics, passed away on March 19. Brockett has done seminal work in applied areas such as robotics, astrodynamics, artificial intelligence, and computer vision or the control of systems at the quantum level. To do this, he promoted areas of mathematics that are also now recognized as one of the reference figures: geometric control theory, dynamical systems, or stochastic calculus.

Roger Brockett was born in 1938, on a farm in the small town of Seville in Ohio (USA), into a large family – he was the youngest of seven brothers. As a child, while other children played with animals, he was interested in agricultural machinery. This early career led him to study engineering because, according to him, it was a subject in which he could cover everything and his obsession in life had always been to understand and comprehend what was around him. In 1964 he received his PhD from Case Institute of Technology (Ohio) with a thesis on dynamical systems and their applications to control. One day, after attending a conference, he stayed for a while talking with the speaker, Peter Elias, chair of the electrical engineering department at the Massachusetts Institute of Technology (MIT). He must have been so impressed that, a few days later, he received a letter offering him a contract at MIT.

It was at MIT, surrounded by some of the best engineers in the world, that Brockett began to excel in both theoretical and applied problem-solving. He studied, for example, the control of satellites, where the nonlinearity of a system determines its time evolution. These systems are described with nonlinear equations. Let’s imagine that we have launched a kite into the air several times; If we launch it twice as fast, the trajectory can be completely different, that is, the second does not follow the first twice as quickly. The complex influence that airflow exerts on the wings of an aircraft makes it very difficult to predict its trajectory. To simplify these complex problems, Roger Brockett analyzed when it is possible to convert a nonlinear system into a linear one, which is much easier to solve. His ideas marked the beginning of a series of theoretical and applied research, which are now being worked on around the world.

Brockett decided to transfer to Harvard University, looking for a new environment to develop his mathematical vision of geometry.

Later, Brockett decided to transfer to Harvard University, looking for a new environment to develop his mathematical vision of geometry and, in his words, “forced me to think more deeply about the basic concepts of science, rather than innovative techniques for solving problems.” In the 1980s, he founded the Harvard Robotics Laboratory, where ambitious projects in the robotic manipulation or control of quantum systems are currently being led. To do this, they use innovative mathematical tools from differential geometry, topology or dynamical systems.

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One of the crucial areas in the current technological development, pioneered by Roger Brockett, is the so-called engineering control theory. It was designed to deal with problems such as those raised by the aviation industry, or those that arise in robot trajectory planning.

To address the nonlinearity inherent in these systems, Brockett used one of the most powerful branches of mathematics, differential geometry. Specifically, it allows calculus techniques, initiated by Isaac Newton and Gottfried Leibniz, to be used for nonlinear spaces, such as a sphere or other curved surfaces, in order to study their intrinsic properties.

His mathematical vision helped him to see, within the complexity of different technological processes, the essential, leaving aside the superfluous, and finding the ideal geometric framework to address it. In this way he was able to design effective techniques to control technological systems to carry out various tasks, or at least see if they were capable of performing them.

Brockett was an exceptional, kind and engaging person to deal with. In his dealings with scientific issues, he was always looking for the essentials, leaving the technical aspects to theory, in his eagerness to understand and comprehend, which has always accompanied him throughout his life.

Their silent contribution has served and will improve our society and our way of life, since their contributions have been fundamental to the topics we now know matter: robotics, satellite control, artificial intelligence … For example, the technologies developed by Brockett and his collaborators offer the perfect way to approach With issues such as reorienting or installing the satellite or bot in the desired position.

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His legacy will live on in the work of the hundreds of scientists around the world who follow in his footsteps. One of the most important aspects of Brockett was undoubtedly the training of posterity. He produced more than sixty doctoral dissertations and some of his students are today scientific leaders in various fields. They include Daniel Lieberzon, Jan Willems, Anthony Bloch, John Barras, John Pellol, David Dobkin, Peter Crouch, and B. s. Krishnaprasad. With all of them and his scientific legacy, Mathematical Engineer Roger Brockett will always be with us.

David Martin De Diego Researcher at the Supreme Council for Scientific Research at the Institute of Mathematical Sciences

Garnet Timon Garcia Longoria He is the coordinator of the ICMAT Sports Culture Unit

Coffee and theories is a section dedicated to mathematics and the environment in which it was created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest developments in this discipline, share points of convergence between mathematics and other social and cultural expressions and remember those who marked their development and knew how to turn coffee into theories . The name evokes Hungarian mathematician Alfred Rennie’s definition: “A mathematician is a machine that turns coffee into theorems.”

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