Roger Brockett

Xi-Ren Cao

Frank Doyle

Hidenori Kimura

Lennart Ljung

Marc Raibert

Roger Brockett

An Wang Professor of Electrical Engineering and Computer Science The School of Engineering and Applied Sciences, Harvard University
BS. MS. and Ph.D. degrees from Case Western Reserve University Professor The Electrical Engineering Department, MIT (19) Editorial Boards and Advisory Committees The IFAC, IEEE, SIAM and AMS
Lecture Series in connection with NATO, CBMS, and NASA meetings
Visiting Positions at more than a dozen universities
Founding Co-Editor of Systems and Control Letters
Author Finite Dimensional Linear Systems
Fellow The IEEE
A Guggenheim Fellowship Study of mathematical system theory
American Automatic Control Council's Richard Bellman award 1989
Elected in the National Academy of Engineering of the USA 1991
IEEE Control Systems Science and Engineering award 1991
Reid Prize in Mathematics from SIAM 1996
Oldenberger Award from the ASME 2004

Nonlinear Control: The Next Decade

As with most engineering subjects, the development of nonlinear control has been driven by the need to solve the technological problems of the day while being limited by the available tools for analysis.?For example, in situations where cost and reliability considerations argued for simple on-off control, approximate methods were developed to guide such designs.?In settings where PID controls were acceptable, stability and loop shaping theories were developed to guide their use.? When computer control became a possibility, trajectory optimization was developed and used, often in concert with system identification.?Thus, in successive waves, we have seen the development of techniques based on Liapunov theory, Hamiltonian-Jacobi theory, functional analysis, differential geometry, etc. These developments have lead to a new and deeper understanding of important problems, such as those arising in adaptive control, robotics and the control of quantum systems. However, looking back at the development of the field, it must be acknowledged that the relationship between the cost of the implementation of a control system and the quality of the trajectories produced by the system has not been squarely addressed.?We argue that this has not only limited technological developments but has also been an impediment in understanding scientific problems such the regulation of the growth and death of cells and how animals control the motion of their bodies.?In this talk we will present a mathematical approach to the problem of jointly optimizing implementation cost and trajectory performance.