The Brockett Legacy Workshop, 2008

Roger Brockett, one of the founders of geometric nonlinear control theory and many other parts of our field, turned 70 on October 22, 2008. To celebrate this occasion, a one-day workshop was held at the 47-th CDC in Cancun, December 8, 2008. The workshop featured eight technical talks on subjects to which Brockett has made fundamental contributions together with many brief remarks and reminiscences by a large number of former students and colleagues.

In addition to the workshop, it is planned to publish several numbers of the journal Communications in Information and Systems in Brockett's honor. Concurrently with the publication of these special issues, all the papers which appear in them will be gathered into a single book that will be separately distributed. The goal of the special issues and book is to provide an archival reference on the current state of the many parts of systems and control where Roger Brockett was either a major contributor or in some cases the originator. The topics treated in the special issues, the book, and the technical part of the workshop reported here below include the stability of nonlinear feedback systems, nonlinear geometric control theory, stochastic systems and nonlinear filtering, the applications of Lie theory to nonlinear systems and control, robotics, formal languages for motion description, computer vision, geodesic and gradient flows on manifolds, information based control and specification complexity, minimum attention control, and quantum control.

Quantum Communication Through Action
-­ A piece of the legacy

John Baillieul
Boston University

Brockett's most far-reaching contributions involved nonlinear geometric control, but his work on what might be called information-based control has also been influential. Several talks explored the boundaries between these areas.

Path Problems in Dynamic Networks: Interplay of Algebraic and Analytic Methods
John Baras
University of Maryland

Brockett's work emphasized the use of mathematics to illuminate technological problems in the most general and ultimately simple way possible.

Nonholonomic Dynamics and Control
Anthony M. Bloch
University of Michigan
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Brockett's work on geometric nonlinear control theory emphasized applications to geometric mechanics.

On Some Model Problems of Quantum Control
Navin Khaneja
Harvard University

While Brockett's early work on geometric nonlinear control emphasized classical mechanics, he has recently been influential in the emerging area of quantum control.

Towards a Unified Framework of Nonlinear Control with Limited Information
Daniel Liberzon
University of Illinois
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Daniel Liberzon speaks about extensions to well-known work he has done with Brockett.

Analyzing an Interesting Hybrid System
A. Stephen Morse
Yale University

Steve Morse ponders an interesting hybrid system.

Happy birthday Roger.

Reminiscences by Friends and Colleagues


Peter Caines and David Mayne recall interactions with Roger at Harvard and Imperial College.

Lyapunov Functions for Systems Described by High Order Differential Equations
Jan C. Willems
Katholieke Universiteit Leuven
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Willems' lecture touched on very early work on which he and Brockett collaborated.

Control Communication Complexity
Wing Shing Wong
Chinese University of Hong Kong

Wing Wong discusses connections of his 1995 collaboration with Roger and his current interest in control communication complexity.

A Colleague of Forty Years
Yu-Chi (Larry) Ho
Harvard University

Larry recalls moments in the leadership role he shared with Roger at Harvard where together they trained well over 100 PhD students.

A Chance for Rebuttal

The workshop concluded with remarks by Roger Brockett in which he recalled his many friendships and collaborations.

Friends and colleagues of nearly half a century gathered to honor Roger Brockett

Wing Wong and Carolann Brockett.

Jan Willems and P.S. Krishnaprasad.

Roger Brockett and Tony Bloch.

Carolann and Roger Brockett share a moment with Alberto Isidori.

Peter Caines ponders a point.

Krishna prepares to introduce the next speaker.

Carolann and Roger at luncheon hosted by Workshop
co-organizer, John Baras.

Joyce and Clyde Martin.