Entropy Analysis of Feedback Control Systems

Abstract

This chapter presents entropy analysis of feedback control systems. Effective use of the entropy (or uncertainty) function proved to be a very formidable tool for evaluating the performance of communication systems. It is perhaps unfortunate that this function offered such powerful solutions to this particular type of problem, because as a result, information theory has remained the private preserve of coding theorists and very little conclusive work has been accomplished in extending the original concepts to other applications. Estimation, feedback control, and adaptive control systems are members of such a class, and clearly many of the components of these systems can be described (at least verbally) as information transformations. More important, common to these types of systems is the use of a sensor or measuring device that is necessary if the desired system performance is to be obtained. This sensor generally monitors the behavior of some process and transmits information about that behavior to another device. The application of entropy techniques to the feedback control problem has led to two important results, the first being a separation theorem and the second being an information theoretic interpretation of the feedback process.