Mathematical Modeling in Industry - A Workshop for Graduate Student, May 26-June 3, 2002

Modeling Networked Control Systems

Principal investigator: Sonja Glavaski
Honeywell
Sonja.Glavaski@honeywell.com

Recently modeling and control of networked control systems with limited communication capability has emerged as a topic of significant interest to controls community. Nature and level of information flow throughout the system is central to a discussion of cooperative control. Applications span wide range, including traffic control, satellite clusters, mobile robotics.

A natural way to model such interconnection topology is as a graph. Each system can be modeled as a node, and arc joins node i and node j if vehicle j is receiving information from vehicle i. To consider all possible topologies it is advisable to use directed graphs, meaning that bi-directional communication is not assumed. In reference [1] it has been demonstrated that a minimal exchange of information between systems can be designed to realize a dynamical system which supplies each individual system with shared reference trajectory. The sensing paths were modeled as a graph, and eigenvalues of the Laplacian matrix of a graph determine the stability of a whole system. In this study quality of communication has not been incorporated.

For coordination of individual systems within networked control system one is especially concerned with acceptable limits of communication network performance. Knowledge of bounds on acceptable network performance is crucial to making networked control system robust in realistic environments. In reference [2] the effects of communication packet losses in the feedback loop of a control system is studied. Motivation for this study has been derived from vehicle control problems where information is communicated via a wireless local area network. A Linear Matrix Inequality condition is developed for the existence of a stabilizing feedback controller. This result can also be used to give a worst-case performance specification (in terms of packet loss rate) for an acceptable communications system.

The focus of our project would be to investigate a possibility of combining these two approaches. Starting form typical directed graph representation of a networked control system we will investigate how to introduce into it a dynamical representation of individual systems and communication network performance. This would allow to systematically address various system performance issues (e.g. stability, observability and controllability).

References:

[1] A. Fax, R.M. Murray. Information Flow and Cooperative Control of Vehicle Formations. Accepted for 2002 IFAC World Congress

[2] P. Seiler and R. Sengupta. Analysis of Communication Losses in Vehicle Control Problems. In Proceedings of the 2001 American Control Conference.

[3] D. Cvetkovic, P. Rowlins, and S. Simic. Eigenspaces Of Graphs, volume 66 of Encyclopedia of Mathematics and Applications, Cambridge University Press, 1997.

[4] Fan R.K. Chung. Spectral Graph Theory

 

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