Electrical & Computer Engineering Faculty Publications

Document Type

Article

Publication Date

12-9-2008

Abstract

In this paper we obtain information theoretical conditions for tracking in linear time-invariant control systems. We consider the particular case where the closed loop contains a channel in the feedback loop. The mutual information rate between the feedback signal and the reference input signal is used to quantify information about the reference signal that is available for feedback. This mutual information rate must be maximized in order to improve the tracking performance. The mutual information is shown to be upper bounded by a quantity that depends on the unstable eigenvalues of the plant and on the channel capacity. If the channel capacity reaches a lower limit, the feedback signal becomes completely uncorrelated with the reference signal, rendering feedback useless. We also find a lower bound on the expected squared tracking error in terms of the entropy of a random reference signal. Examples and simulations are provided to demonstrate the results.

Publisher

IEEE

Publication Title

Decision and Control

ISSN

0191-2216

First Page

3626

Last Page

3632

Language (ISO)

English

Keywords

channel capacity, closed loop systems, eigenvalues and eigenfunctions

Download

Share

COinS