Observability and stabilisability of networked control systems with limited data rates

ABSTRACT

This paper investigates the observability and stabilisability problem for linear time-invariant systems, where sensors and controllers are geographically separated and connected by a stationary memoryless digital communication channel. The limited information of the plant state is transmitted over such a channel to the controller. We focus on explaining the effect imposed by limited data rates. A new quantisation, coding and control scheme is presented to minimise the required data rate for observability and stabilisability. Different from prior research, our study shows that, the required data rate is determined by the state prediction error. Namely, the smaller prediction error requires the smaller codeword length, which leads to the smaller data rate. It is shown that, there exists a lower bound on the average data rate above which the system is observable and stabilisable. Illustrative examples are given to demonstrate the effectiveness of the proposed quantisation, coding and control scheme.

KEYWORDS:

• Limited data rates
• observability
• stabilisability
• networked control systems

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Qingquan Liu   http://orcid.org/0000-0003-4952-8079

Rui Ding http://orcid.org/0000-0002-5698-4358

Additional information

Notes on contributors

Qingquan Liu

Qingquan Liu received the B.S. degree from Nanjing University of Science and Technology, Nanjing, China, in 1998, and the M.S. degree and Ph.D. degree from Northeastern University, Shenyang, China, in 2008 and in 2012, respectively. From 2012 to 2015, he was a postdoctoral researcher at Chinese Academy of Sciences, China. In 2013, he became the head of Department Information Counter Teaching and Research of Shenyang Ligong University, Shenyang, China. He is currently an associate professor in College of Equipment Engineering at Shenyang Ligong University, Shenyang, China. His research interests lie in the intersection of communication, control, and information theory. His current research is in networked control, quantised feedback control, and robust control.

Rui Ding

Rui Ding received the B.S. degree from Shenyang ligong University, Shenyang, China, in 2017. Now, he is a postgraduate in College of Equipment Engineering at Shenyang Ligong University, Shenyang, China. His research interests lie in nonlinear control systems and networked control systems.