## Brockett, Roger

#### Research Interests

**Applied Mathematics & Computational Science:** Control Theory and Stochastic Systems**Computer Science:** Intelligent Systems and Computer Vision**Electrical Engineering:** Robotics and Control

#### Background

As high-data-rate sensing mechanisms have proliferated and the value of autonomous decision making has become more widely recognized, many sophisticated techniques have been applied to process data within feedback loops. As a result, interest in estimation and control algorithms suitable for time-critical applications has grown. Professor Brockett's research is concerned with the development of prototype modules and general principles that can be used to design such systems and to predict how they will interact with their environment.

Robots are one example of computer-controlled machines in which motion control is a central issue. Others include surveillance vehicles, numerically controlled machine tools, autonomous loaders, repair vehicles, etc. Many recent efforts to permit these systems to react to various sensory data in real time incorporate new computational paradigms, such as neural networks and adaptive arrays. In recent work, Professor Brockett and his coworkers have shown how parallel analog algorithms can be used for these purposes and how several problems in combinatorial optimization can be understood in the context of control and dynamical systems.

Problems of computational tractability are critical to systems that must operate in real time. An answer that cannot be computed in a fixed amount of time may be useless. To operate within these constraints, systems must reduce data as they are gathered, making use of special data structures that facilitate rapid computation. One goal of current research is the development of a device-independent language to control such systems and to model in a useful way systems that are language driven.

#### Honors and Awards

**Fellows**

National Academy of Engineering, 1991

Institute of Electrical and Electronics Engineers, 1974

**Other awards**

Capers and Marion McDonald Award for Excellence in Mentoring and Advising, 2011

IEEE Leon K. Kirchmayer Graduate Teaching Award, 2009

Rufus Oldenburger Medal from the American Society of Mechanical Engineers, 2005

W.T. and Idalia Reid Prize in Mathematics from the Society for Industrial and Applied Mathematics, 1996

IEEE Field award in Systems Science and Engineering, 1991

IEEE Control Systems Award, 1991

Richard E. Bellman Control Heritage Award from the American Automatic Control Council, 1989

#### Selected Publications

R. W. Brockett, Dynamical Systems and Their Associated Automata" in Systems and Networks: Mathematical Theory and Applications, (U. Helmke, et al. Eds.) Akademie Verlag, Berlin, 1994.

R. W. Brockett and Andrew Blake "Estimating the Shape of a Moving Contour,"Proceedings of the 1994 IEEE Conference on Decision and Control, December, 1994.

R. W. Brockett, "Language Driven Hybrid Systems," Proceedings of the 1994 IEEE Conference on Decision and Control, December, 1994.

R. W. Brockett and P. Maragos, "Evolution Equations for Continuous Scale Morphology," IEEE transactions on Signal Processing Vol. 42, (1994) pp. 3377-3386.

R. W. Brockett, "Hybrid Models for Motion Control Systems," in Perspectives in Control, (H. Trentelman and J. C. Willems, Eds), Birkh, Boston, 1993, pp. 29-54.

R. W. Brockett, "Smooth Dynamical Systems Which Realize Arithmetical and Logical Operations," in Lecture Notes in Control and Information Sciences. Three Decades of Mathematical Systems Theory. (H. Nijmeijer and J.M. Schumacher, Eds.) Springer-Verlag, Berlin, 1989, pp. 19-30.

R. W. Brockett, "Dynamical Systems That Sort Lists, Diagonalize Matrices and Solve Linear Programming Problems," Linear Algebra and Its Applications, 146, 1991, pp. 79-91.

R. W. Brockett, "Dynamical Systems That Learn Subspaces," in Mathematical System Theory: The Influence of R.E. Kalman, (A.C. Antoulas, Ed.) Springer-Verlag, Berlin, 1991, pp. 579-592.

R. W. Brockett, "An Estimation Theoretic Basis for the Design of Sorting and Classification Networks," in Neural Networks, (R. Mammone and Y. Zeevi, Eds) Academic Press, 1991, pp. 23-41.

R. W. Brockett and A. Stokes, "On the Synthesis of Compliant Mechanisms," Proceedings of the 1991 IEEE Conference on Robotics and Automation, IEEE, New York, 1991.