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Limits on the Network Sensitivity Function for Multi-Agent Systems on a Graph

Tonetti, Stefania and Murray, Richard M. (2009) Limits on the Network Sensitivity Function for Multi-Agent Systems on a Graph. California Institute of Technology , Pasadena, CA. (Unpublished)

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This report explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason's Direct Rule. Explicit forms for special types of graphs are presented. An analysis of the role of cycles points out that these structures influence and limit considerably the performance of the system. The more the cycles are equally distributed among the formation, the better performance the system can achieve, but they are always worse than the single agent case. We also prove the networked version of Bode's integral formula, showing that it still holds for multi-agent systems.

Item Type:Report or Paper (Technical Report)
Murray, Richard M.0000-0002-5785-7481
Additional Information:The authors would like to thank Håkan Terelius and Anna Maria Cherubini for their feedback on the material in this paper.
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:2009.001
Persistent URL:
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28137
Deposited By: Imported from CaltechCDSTR
Deposited On:03 Nov 2009
Last Modified:18 Mar 2015 23:00

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