The Duality between Estimation and Control
In this talk, I present a solution to the long-standing problem of giving a rigorous interpretation of the Duality between Estimation and Control for nonlinear diffusion processes . This constitutes a vast generalization of the formal duality between linear filtering for gaussian processes and linear quadratic optimal control . These results are based on a variational formulation of Bayesian inference for random variables taking values in Polish spaces . This variational problem admits a dual variational problem in terms of Legendre-Fenchel Duality . There are close connections of these ideas with the Gibbs Variational Principle of Statistical Mechanics where translation invariant Gibbs Measures are characterized in terms of minimization of Free Energy .
Sanjoy K. Mitter received his Ph.D. degree from the Imperial College of Science and Technology in 1965. He taught at Case Western Reserve University from 1965 to 1969. He joined MIT in 1969 where he has been a Professor of Electrical Engineering since 1973. He was the Director of the MIT Laboratory for Information and Decision Systems from 1981 to 1999. He has also been a Professor of Mathematics at the Scuola Normale, Pisa, Italy from 1986 to 1996. He has held visiting positions at Imperial College, London; University of Groningen, Holland; INRIA, France; Tata Institute of Fundamental Research, India and ETH, Zürich, Switzerland; and several American universities. Professor Mitter has been awarded the AACC Richard E. Bellman Control Heritage Award for 2007. He was the McKay Professor at the University of California, Berkeley in March 2000, and held the Russell-Severance-Springer Chair in Fall 2003. He is a Fellow of the IEEE and a Member of the National Academy of Engineering. He is the winner of the 2000 IEEE Control Systems Award. He was elected a Foreign Member of Istituto Veneto di Scienze, Lettere ed Arti in 2003. In 1988, he was elected to the National Academy of Engineering.
His current research interests are Communication and Control in a Networked Environment, the relationship of Statistical and Quantum Physics to Information Theory and Control and Autonomy and Adaptiveness for Integrative Organization.