Regular Source Coding for Communication Constrained

Feedback Channels

Professor John Baillieul

Boston University

College of Engineering

It has been conclusively established that the so called data-rate theorem imposes fundamental limits on stability in terms of the information capacity of the feedback channel. Moreover, it is known that the data-rate inequality is strict and can be

achieved exactly by carefully designed source coding of feedback signals. Within the restricted class of codes which can achieve the data-rate bound exactly, some are preferable across a range of data-rates. In his recent Ph.D. thesis, Keyong Li introduced what are called regular quantizations. Feedback control laws that use regular quantizations have the property that as channel capacity becomes large, the feedback law achieves asymptotic stability to an arbitrarily close approximation. Li's thesis gives a complete characterization of regular quantizations for scalar systems. In this talk, new results on regular quantization for multidimensional linear systems will be presented. These shed light on quantized control design which is not revealed by scalar systems. For a class of 2-dimensional systems, standard quantizations of classical designs which place closed-loop poles close to the right-half plane are seen to be non-regular. In the limit, as closed loop poles tend toward the right half plane, it can be shown that a bounded response requires the number of quantization levels to increase.

Friday, October 13, 2006

3:30 – 4:30 p.m.

1500 EECS