Document Type

Journal Article

Date of this Version

4-1-2013

Comments

@INPROCEEDINGS{wcn_jsac13, author = {Miroslav Pajic and Shreyas Sundaram and Rahul Mangharam and George J. Pappas}, title = {Topological conditions for in-network stabilization of dynamical systems}, booktitle = {IEEE Transactions in Selected Areas of Communications (JSAC)}, volume = 31, pages = {794-807}, number = 4}, year = {2013}, month = {April}}

Abstract

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.

Keywords

Networked control systems, decentralized control, wireless sensor networks, structured systems, in-network control, network coding, cooperative control

 

Date Posted: 05 July 2013

This document has been peer reviewed.