In this talk I discuss the issue of Information Flow from the noisy observations of the dynamical system, to the estimator, controller and back to the system through the actuator. Is the flow informationally conservative or dissipative? Is there an analogue of the Dissipation Inequality (in the sense of Willems) but in Information terms for the flow? I first discuss my earlier work with Nigel Newton on this question in the context of the Kalman Filter (generalizable to the nonlinear situation). It can be shown that the Kalman Filter stores the minimal amount of information (Shannon) to interpret the present and predict the future and discards historical information at an optimal rate governed by the Fisher Information. In this sense the Kalman Filter is informationally optimal. I then discuss these questions in the context of controlled filters by considering the problem of extracting maximum amount of work from a Noisy Electrical Circuit using information from an appropriate filtering process. There are important connections of these ideas to current work on Nonequlibrium Statistical Mechanics (Joint work with Henrik Sandberg, Jean-Charels Del Venne and Nigel Newton). I conjecture that these ideas are relevant to understanding Self-Tuning Regulators and Stochastic Adaptive Control from an “Information” viewpoint.
Prof. Sanjoy Mitter is with the Department of EECS at MIT. He received his Ph.D. from Imperial College, London, in 1965 and taught at Case Western Reserve Uni. from 1965 to 1969 before joining MIT in 1969. His research has been concerned with Systems, Control and Communication. He has served as the director for the Center for Intelligent Control and the Lab. for Information and Decision Systems. He received both the Richard E. Bellman Control Heritage Award from the American Automatic Control Council (2007) and the IEEE Control Systems Award (2000). He was elected a member of the National Academy of Engineering in 1988.