Information and Entropy Flow in Filtering and Control

Recent applications such as control over networks, system state estimation using networks of sensors and real-time embedded control systems have blurred the boundaries of the disciplines of communications, control and computation. Increasingly, communication, control and computation take place through interconnection of systems leading to desirable interactions. From a methodological point of view, simple models where the nature of these desirable interactions can be studied in some depth are needed. We examine the structure of interaction between sensing, communicating and controlling in the context of statistical filtering for signals described as Hidden Markov processes and in the context of stabilization of an unstable control system where the sensor and controller are linked via a noisy communication channel. We argue amongst other things, that a fundamental reexamination of information theory is needed to address these questions. These ideas appear to have nontrivial connections to recent work in nonequilibrium statistical mechanics.