Analysis & Design of Control for Distributed Embedded Systems under Communication Constraints — — –

The Networked Embedded Control System (NECS) uses communication networks in the feedback loops. Since the embedded systems have the limited battery power along with limited bandwidth and computing power, the feedback data rates are limited. The rate of communications can drastically affect system stability. Hence, there is a strong need for understanding and merging the Control Theory with Communication or Information Theory. The data rate constraint introduces quantization into the feedback loop whereas the communication or computational model induces discrete events which are no more periodic. These two phenomena give the NECS a twofold nature : continuous and discrete, and render them specific. In this thesis we analyze the stability and performance of NECS from Informationtheoretic point of view. For linear systems, we show how fundamental are the tradeoffs between the communication-rate and control goals, such as stability, controllability / observability and performances. An integrated approach of control and communication (in terms of Shannon Information Rate) of NECS or distributed embedded control systems is studied. The main results are as follows : • We showed that the entropy reduction which is same as uncertainty reduction is dependent on Controllability Gramian only. It is also related to Shannon MutualInformation. • We demonstrated that the gramian of controllability constitutes a metric of information theoretic entropy with respect to the noises induced by quantization. Reduction of these noises is equivalent to the design methods proposing a reduction of the controllability gramian norm. • We established a new relation of Fisher Information Matrix (FIM) and Controllability Gramian (CG) based on estimation-theoretic and information-theoretic explanations. • We propose an algorithm which optimally distributes the network capacity between a number "n" of competing actuators. The metric of this distribution is the Controllability Gramian.