Joint Optimization of Communication Rates and Linear Systems

L. Xiao, M. Johansson, H. Hindi, S. Boyd, and A. Goldsmith

IEEE Transactions on Automatic Control, 48(1):148-153, January, 2003.
Shorter version appeared in Proceedings Conference on Decision and Control, p2321-2326, December 2001.
A longer version, with title Joint Optimization of Communications Systems and Networked Feedback Systems, appeared as chapter 11 of Switching and Learning in Feedback Systems, Lecture Notes on Computer Science 3355, R. Murray-Smith and R. Shorten, editors, pages 248-272, Springer 2005.

We consider a linear control system in which several signals are transmitted over communication channels with bit-rate limitations. With the coding and medium access schemes of the communication system fixed, the achievable bit-rates are determined by the allocation of communications resources such as transmit powers and bandwidths, to different communication channels. We model the effect of bit-rate limited communication channels by uniform quantization, and the quantization errors are modeled by additive white-noises whose variances depend on the achievable bit-rates. We optimize the stationary performance of the linear system by jointly allocating resources in the communication system and tuning parameters of the controller.