A Framework for Control System Design Subject to Average Data-Rate Constraints

• Published in: IEEE transactions on automatic control Vol. 56; no. 8; pp. 1886 - 1899
• Main Authors: Silva, E. I., Derpich, M. S., Ostergaard, J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Average data-rate; Channel coding; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Control system synthesis; Control systems; Control systems design; Control theory; Control theory. Systems; Decoding; Entropy; Exact sciences and technology; Feedback; Focusing; Linear systems; Mutual information; networked control systems; perfect reconstruction; Process control. Computer integrated manufacturing; Quantization; Rate-distortion; signal-to-noise ratio; Silicon; Software; Stability; Studies; System theory; perfect reconstruction; Feedback regulation; Control synthesis; Entropy; Distributed system; Information control; Absolute stability; Average data-rate; Discrete time; signal-to-noise ratio; Distributed control; networked control systems; Quantifier; Transfer function; State constraint; Signal to noise ratio; Information theory
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2010.2098070

This paper studies discrete-time control systems subject to average data-rate limits. We focus on a situation where a noisy linear system has been designed assuming transparent feedback and, due to implementation constraints, a source-coding scheme (with unity signal transfer function) has to be deployed in the feedback path. For this situation, and by focusing on a class of source-coding schemes built around entropy coded dithered quantizers, we develop a framework to deal with average data-rate constraints in a tractable manner that combines ideas from both information and control theories. As an illustration of the uses of our framework, we apply it to study the interplay between stability and average data-rates in the considered architecture. It is shown that the proposed class of coding schemes can achieve mean square stability at average data-rates that are, at most, 1.254 bits per sample away from the absolute minimum rate for stability established by Nair and Evans. This rate penalty is compensated by the simplicity of our approach.