Roger Brockett is the An Wang professor of electrical engineering and Computer Science at Harvard University. He has been exploring questions in engineering and applied sciences since starting graduate school, and has been teaching since his appointment as an Assistant Professor at MIT in 1963. His contributions include early work on frequency domain stability theory (multipliers), circle criterion instability, differential geometric methods in nonlinear control, feedback linearization and stabilization, the computation of Volterra series, a Lie algebra approach to the sufficient statistics problem in nonlinear estimation, work on robot kinematics and dynamics, formal languages for motion control, hybrid systems, flows for computation related to integrable systems, sub-Riemannian geometry, minimum attention control, quantum control, quantized systems and, most recently, optimal control of Markov processes. He is a fellow of the IEEE and of SIAM, has received awards from IEEE (Control Systems Science and Engineering), ASME (Oldenberger), SIAM (Reid Prize), and AACC (Eckman, and Bellman), is a member of the US National Academy of Engineering. He is this year recipient of the IEEE Leon Kirchmayer Award for Graduate Education. He has directed approximately 60 Ph.D. theses and authored about 200 research papers.
It is widely recognized that many of the most important challenges faced by control engineers involve the development of methods to design and analyze systems having components most naturally described by differential equations interacting with components best modeled using sequential logic. This situation can arise both in the development of high volume, cost sensitive, consumer products and in the design and certification of one of a kind, complex and expensive systems. The response of the control community to this challenge includes work on limited communication control, learning control, control languages, and various efforts on hybrid systems. This work has led to important new ideas but progress has been modest and the more interesting results seem to lack the kind of unity that would lead to a broadly inclusive theory. In this talk we describe an approach to problems of this type based on sample path descriptions of finite state Markov processes and suitable adaptations of known results about linear systems. The result is an insightful design technique yielding finite state controllers for systems governed by differential equations. We illustrate with concrete examples.