Limitations of linear control over packet drop networks

Nicola Elia, Jeff N. Eisenbeis

Research output: Contribution to journalArticlepeer-review

68 Scopus citations

Abstract

In this paper, we investigate control across stochastic dropout channels. In particular, we consider the Mean Square Stability of a SISO plant in the case there is only one channel in the feedback loop and the case where both actuator and sensor channels are present. We seek optimal networked control schemes that are memoryless functions of channel state information and for each channel state are otherwise linear and time invariant functions of channel output. We establish a fundamental limit on the dropout probability allowable for the Mean Square Stability of the closed loop system. The maximal tolerable dropout probability is only a function of the unstable eigenvalues of the plant. When either the actuator or the sensor channel is present, we propose a receiver structure that can stabilize the system under the worst dropout probability; moreover, we can simultaneously design the optimal controller and receiver and show that they can be implemented in physically separated locations (decentralized). When both actuator and sensor channels are present in the loop, the main result is a centralized stabilization technique that always achieves the fundamental bound via noiseless acknowledgement from the actuation receiver. Finally, we extend the results to the more general case where also the acknowledgements are lost with a given probability and compute how the unreliable delivery of the acknowledgements affects the minimal quality of service required of the actuator and sensor channels.

Original languageEnglish (US)
Article number5585719
Pages (from-to)826-841
Number of pages16
JournalIEEE Transactions on Automatic Control
Volume56
Issue number4
DOIs
StatePublished - Apr 2011
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received February 02, 2006; revised June 29, 2010; accepted September 16, 2010. Date of publication September 27, 2010; date of current version April 06, 2011. This work was supported by NSF under the Career Award Grant ECS-0093950. Recommended by Associate Editor E. Jonckheere. N. Elia is with the Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50010 USA (e-mail: nelia@iastate.edu). J. N. Eisenbeis is currently with the Department of Math Sciences, Carnegie Mellon University, Pittsburgh, PA 15213 USA (e-mail: jeisenbe@andrew.cmu. edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAC.2010.2080150

Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

Keywords

  • Control over packet drop networks
  • mean square stability
  • networked control
  • quality of service

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