Skip to main content

Topological conditions for in-network stabilization of dynamical systems

Publication ,  Journal Article
Pajic, M; Mangharam, R; Pappas, GJ; Sundaram, S
Published in: IEEE Journal on Selected Areas in Communications
April 4, 2013

We study the problem of stabilizing a linear system over a wireless network using a simple in-network computation method. Specifically, we study an architecture called the Wireless Control Network (WCN), where each wireless node maintains a state, and periodically updates it as a linear combination of neighboring plant outputs and node states. This architecture has previously been shown to have low computational overhead and beneficial scheduling and compositionality properties. In this paper we characterize fundamental topological conditions to allow stabilization using such a scheme. To achieve this, we exploit the fact that the WCN scheme causes the network to act as a linear dynamical system, and analyze the coupling between the plant's dynamics and the dynamics of the network. We show that stabilizing control inputs can be computed in-network if the vertex connectivity of the network is larger than the geometric multiplicity of any unstable eigenvalue of the plant. This condition is analogous to the typical min-cut condition required in classical information dissemination problems. Furthermore, we specify equivalent topological conditions for stabilization over a wired (or point-to-point) network that employs network coding in a traditional way-as a communication mechanism between the plant's sensors and decentralized controllers at the actuators. © 1983-2012 IEEE.

Duke Scholars

Published In

IEEE Journal on Selected Areas in Communications

DOI

ISSN

0733-8716

Publication Date

April 4, 2013

Volume

31

Issue

4

Start / End Page

794 / 807

Related Subject Headings

  • Networking & Telecommunications
  • 4606 Distributed computing and systems software
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0805 Distributed Computing
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Pajic, M., Mangharam, R., Pappas, G. J., & Sundaram, S. (2013). Topological conditions for in-network stabilization of dynamical systems. IEEE Journal on Selected Areas in Communications, 31(4), 794–807. https://doi.org/10.1109/JSAC.2013.130415
Pajic, M., R. Mangharam, G. J. Pappas, and S. Sundaram. “Topological conditions for in-network stabilization of dynamical systems.” IEEE Journal on Selected Areas in Communications 31, no. 4 (April 4, 2013): 794–807. https://doi.org/10.1109/JSAC.2013.130415.
Pajic M, Mangharam R, Pappas GJ, Sundaram S. Topological conditions for in-network stabilization of dynamical systems. IEEE Journal on Selected Areas in Communications. 2013 Apr 4;31(4):794–807.
Pajic, M., et al. “Topological conditions for in-network stabilization of dynamical systems.” IEEE Journal on Selected Areas in Communications, vol. 31, no. 4, Apr. 2013, pp. 794–807. Scopus, doi:10.1109/JSAC.2013.130415.
Pajic M, Mangharam R, Pappas GJ, Sundaram S. Topological conditions for in-network stabilization of dynamical systems. IEEE Journal on Selected Areas in Communications. 2013 Apr 4;31(4):794–807.

Published In

IEEE Journal on Selected Areas in Communications

DOI

ISSN

0733-8716

Publication Date

April 4, 2013

Volume

31

Issue

4

Start / End Page

794 / 807

Related Subject Headings

  • Networking & Telecommunications
  • 4606 Distributed computing and systems software
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0805 Distributed Computing